The London stadium was stunned as the Serbian side took the lead just minutes after the restart as Petar Stanic latched on to a mistake by Angelo Ogbonna.
The comeback was started after 66 minutes when Nemanja Petrovic turned the ball into his own net from an excellent Said Benrahma cross.
Just four minutes later Mohammed Kudus scored his first West Ham goal following his summer move from Ajax, heading home a trademark James Ward-Prowse corner to put the Hammers ahead.
Tomas Soucek finished off the visitors with an excellent header past Nikola Simic from Ward-Prowse's corner.
The Serbian league leaders did make life difficult for the hosts with some great defending and made them work hard for the points.
This was the Irons' first European game since the famous night in Prague where they won the Europa Conference League against Fiorentina.
Here are the player ratings from West Ham's victory over Backa Topola.
West Ham
Lukasz Fabianski - 7
The Polish goalkeeper could not have done much about the visitors' goal, rushing out to close Stanic. The former Arsenal shot-stopper did not have much to do throughout as the Hammers dominated the ball.
Thilo Kehrer - 6
Kehrer picked up a yellow card early on in the match after a poorly timed tackle, which left him in a precarious position for the rest of the match.
The German defender went close to scoring the opener in the 17th-minute after firing the ball between bodies towards goal, but was denied by an excellent save by Simic.
The Greek defender looked fairly assured on his debut for the club, cleaning up the limited attacks that the hosts faced well and playing it forward quickly. Mavropanos will face much harder tasks going forward as he was not tested much.
Angelo Ogbonna - 3
Ogbonna looked suspect both on and off the ball throughout and made a huge error to gift the visitors their first goal.
The captain on the night was too slow and hesitant, which allowed Stanic to muscle him off the ball, before running through and slotting past Fabianski.
For the rest of the game, the Italian looked nervous that he'd make another mistake.
Aaron Creswell - 5
Cresswell struggled to have much of an impact on the game going forward and created little down the left-hand side.
The full-back did well to ensure West Ham did not concede in injury time of the first half, but was unable to continue at the interval and was replaced by Emerson Palmieri.
The former Southampton midfielder has been a revelation at West Ham since signing in the summer window and continued his excellent form on the night.
Ward-Prowse picked up two assists with two brilliant deliveries into the box for Kudus and Soucek to both head home. The hosts looked a threat every time the number seven stepped over a set-piece.
Pablo Fornals - 4
Fornals did not have any real impact on the match and struggled to create for the players in front of him.
The Spanish midfielder gave the ball away too many times, which broke down attacks, and West Ham looked much better when he was replaced after an hour by Michail Antonio.
Lucas Paqueta - 4
Much like Fornals, Paqueta found it hard to find any space in the midfield and was sloppy on the ball throughout. The Brazil international has been excellent so far this season but was unable to reach those standards tonight.
Paqueta should have scored after Mavropanos knocked the ball down but was unable to reach the ball.
Mohammed Kudus - 8
Kudus had a very promising full debut and showed West Ham fans what they can expect moving forward from their summer signing.
The Ghana international was unlucky not to be awarded the equaliser as the ball was adjudged to have flicked off Nemanja Petrovic. Kudus wasted no time, though, scoring his first goal in Claret and Blue minutes later with a great header from a Ward-Prowse corner.
The winger showed some electric pace and tricky dribbling at times to beat his defender.
Danny Ings - 4
Ings looked off the pace whilst he was on the pitch and failed to provide either a goal threat or a focal point for his side.
West Ham lacked a physical presence up front that they are usually able to rely on when Antonio is playing and they looked much more threatening when the Jamaican entered the pitch.
Said Benrahma - 6
The Algerian international struggled in the first half to find space to create, but produced a moment of magic to help the hosts bring the game back level.
Benrahma faked a cross to create a bit of space before whipping a dangerous ball across the box which Petrovic turned into his own net.
Substitutes
Emerson (Cresswell 46') - 6
Emerson replaced Cresswell at half-time and provided much more of a threat down the left, helping out Benrahma a lot more than the man he replaced.
The former Chelsea defender did not have a lot of defending to do as West Ham had complete control for most of the second half.
Michail Antonio (Fornals 61') - 4
Although Antonio provided more of a threat than Ings, he could have had at least two goals with some better finishing.
Paqueta and Ings both provided the forward with chances but sloppy touches meant he was unable to score on both occasions.
Tomas Soucek (Ings 77') - 8
Soucek had an excellent cameo, killing the game off within five minutes of entering the pitch; flicking the ball into the far corner with his head from Ward-Prowse's corner. The Czech international provided physicality in the midfield to help West Ham see out the match.
Maxwel Cornet - (Paqueta 86') - N/A
Backa Topola
Nikola Simic - 7
The visitor's number one made some excellent saves throughout the first half from Ings, Paqueta and Kehrer to keep the hosts at bay. Simic was unlucky to concede three goals and could not have done much about any of the goals.
Milos Cvetkovic - 5
The full-back defended valiantly throughout the first half keeping Benrahma quiet, but was overwhelmed in the second half.
Mateja Dordevic - 4
Like the rest of the visitors' defence, Dordevic defended resolutely in the first half but struggled to deal with West Ham's attack in the second.
Dordevic made a sloppy challenge that allowed Benrahma to beat him, and subsequently injure him, to set up the first goal.
Nemanja Stojic - 6
Stojic went close with a header just before half-time, hitting the top of the crossbar. However, the centre-back found it hard to win many tackles or intercept the ball much.
Goran Antonic - 4
The defender did well in the first half to keep West Ham's forwards at bay but became overwhelmed throughout the game as the attacks became more and more relentless.
Nemanja Petrovic - 4
The full-back had a difficult time up against Kudus, who was constantly running at him and threatening to either run past him or get in behind.
Petrovic also scored an own goal to allow West Ham to equalise, turning in Benrahma's cross into his own net.
Milan Radin - 5
Backa Topola's midfield struggled to gain any control on the match and were completely dominated by West Ham's.
Radin was guilty of losing the ball too many times and lacked composure in the rare times he found himself with the ball in space.
Nikola Kuveljic - 4
Kuveljic picked up an early yellow card which stopped him from being able to put many challenges in, and much like the rest of the visitors' midfield, he was sloppy on the ball.
Ifet Djakovac - 5
The midfielder struggled to have an impact on the game and barely touched the ball throughout.
Petar Stanic - 7
The forward did brilliantly to knock Ogbonna off the ball and ran through before slotting the ball perfectly past Fabianski to put his side ahead just after half time.
Stanic finished very confidently leaving the goalkeeper with absolutely no chance.
Sasa Jovanovic - 6
Jovanovic was the more threatening of the two strikers for the Serbian league leaders and was very close to setting up a goal just before half time.
The forward produced an excellent flick-on from a corner, but the ball just wouldn't fall to his teammate at the back post.
Substitutes
Vukasin Krstic (on for Dordevic 69') - 4
The visitors conceded two goals soon after he came on and he struggled to deal with the power of Antonio and Kudus.
Aleksandar Cirkovic (for Djakovac 80') - N/A
Milos Vulic (for Kuveljic 80') - N/A
Marko Rakonjac (for Petrovic 81') - N/A
Martin Mircevski (for Jovanovic 90+2') - N/A
