Jose Mourinho's side found it hard to break down the home side and it was Owen Coyle's men who broke the deadlock. Danny Graham and Marvin Emnes combined as the Dutchman set up the Rovers top scorer and he didn't disappoint to make it 1-0.
However, just about ten minutes later, Rovers were made to pay for their defensive complacency as Henrikh Mkhitaryan sent Marcus Rashford on his way towards goal with a delightful through ball. Rashford slotted it past the oncoming Jason Steele to make it 1-1.
The second-half was where United dominated the game. Mourinho's changes at the hour mark, bringing on Paul Pogba and Zlatan Ibrahimovic, made the difference as the duo combined once again to devastating effect.
Just as the game seemed headed for a draw, Pogba came up with a delightful lofted pass to pick out Ibrahimovic.
The Swede then took his time and slotted the ball to the right of Steele to make it 2-1 and give the visitors the victory they so craved.
The victory ensured the Red Devils are progressing well in all of their cup competitions.
United face Chelsea in the next round, a match that will tell us a lot about how far the side has come since their 4-0 drubbing at the hands of Antonio Conte's side earlier this season.
But how did United fare in their fifth-round win at Blackburn?
Goalkeeper and defence
Sergio Romero - (7/10) - Romero has been the man for United's cup ventures this season and the Argentine started again here with David De Gea given a rest by Mourinho. Romero had to be on alert for much of the game as Blackburn looked threatening on the counter and tested Romero with a few good efforts. Graham's goal came as a product of a defensive mistake from Marcos Rojo and there wasn't much Romero could do about it. He was solid for the rest of the game and completed another 90 minutes in goal.
Ashley Young - (7/10) - Young started the game at right-back as Mourinho opted to rest Antonio Valencia for this one. Young's game was overall very effective. He was excellent going forward for the Red Devils and showed shades of the old Young as he constantly looked to get down the wings and put in a decent cross. His defensive work-rate was excellent but he was caught out of position on a few occasions, which allowed the Rovers attackers to get forward on the right-hand side.
Chris Smalling - (6/10) - Smalling continued at the back for United as he aims to find his top form once again for the Red Devils. United's defence as a whole looked surprisingly unconvincing as Rovers were always effective on the counter and were able to trouble the top-flight outfit time and again. It wasn't a commanding performance from Smalling, but it was job done well enough by the England international.
Marcos Rojo - (6/10) - Rojo has been one of the revelations of Mourinho's reign so far this season. The Argentine has been a rock at the back for United, performing well and gelling well with whoever is lined up alongside him. However, the game against Rovers was a less-inspiring display from the former Sporting CP man. He was beaten with ease by Emnes leading to Blackburn's goal and he could've remained more solid in blocking off the Dutchman. His intention to press the ball and win it back as soon as it was lost was one of the key reasons why the home side's attackers were able to find spaces to exploit. Much like his partner in crime Smalling, Rojo had an unconvincing game.
Matteo Darmian - (7/10) - Darmian was afforded yet another rare start by Mourinho as the Italian was the one opted for over the returning Luke Shaw, who was left on the bench. Darmian was certainly one of United's better performers in a defensive sense, however his offensive play left much to be desired. The Italian international is not well-known for his attacking prowess and showed everyone why here, as much of United's attacks down the flanks were down the right through Young. However, Darmian was solid defensively and was rarely caught out by the home side's forwards.
Michael Carrick - (7/10) - Carrick starting in the game may have come as something of a surprise as some expected Bastian Schweinsteiger to start. However, veteran Carrick played the whole ninety minutes of the game and dictated the game from the middle of the park. He was pressed by Emnes early on in the game and wasn't afforded the space he needed, but soon found his feet in the game. It was a decent outing for the 35-year-old overall.
Ander Herrera - (6/10) - Herrera started alongside Carrick in a two-man midfield and went about his usual box-to-box play well. The Spaniard tried to test Steele with some efforts from long-range but couldn't do much otherwise. A relatively quieter outing from the midfield dynamo.
Jesse Lingard - (7/10) - Lingard started the game as part of an exciting four-man attack but failed to match the expectations of the fans. Lingard started off on the right-side but was rotating positions with his fellow midfielders constantly and was always on the move to give the Rovers midfield and defence problems in tracking his movements. He was taken off on the hour mark for Pogba after a wasteful hour in which he failed to provide the final ball in many a situation.
Henrikh Mkhitaryan - (9/10) - Mkhitaryan was deployed as a No.10 by Mourinho for this one and in his favoured position, the Armenian played some delightful football. His work-rate all over the opposition's half in dictating United's attacks was instrumental and it was his well-timed through ball that sent Rashford on his way to get the equaliser for his side. His skill on the ball was mesmerising at time but he lacked the final ball on a few occasions, which might have prevented him from getting on the scoresheet. He completed the 90 minutes on the pitch once again as he finally seems to have established himself as a favourite in Mourinho's eyes.
Anthony Martial - (6/10) - Martial, as many had expected, started this game for United as Mourinho aims to give as much cup football to the Frenchman as possible. However, for this one, Martial didn't look like his best self. Just like his fellow attackers, he lacked the final ball to punish the opposition. He was taken off at the hour mark for Ibrahimovic as Mourinho aimed to cement the result and get the job done in a move to avoid a replay game, as the game was stuck at 1-1 at the time.
Marcus Rashford - (8/10) - Rashford started yet another cup game for the Red Devils up top as he continues to get appearances in his first full season with the senior team. His pace up top caused the Rovers defence a few problems and it was his goal that brought United back in the game. He latched on to Mkhitaryan's perfectly-timed ball and took his equaliser well. He was taken off in the last few minutes of the game for Juan Mata, a move aimed at seeing the game out.
Zlatan Ibrahimovic - (9/10) - Ibrahimovic was sent off the bench by Mourinho with one and only one objective: score a goal and finish the game. That's exactly what Ibrahimovic did with his one real chance in the game. It was a brilliant lofted ball from Pogba that set up the Swede for his shot. The former Paris Saint-Germain man waited for the ball to drop back down and executed his attempt to perfection, firing into the bottom corner to give United the lead. Job done.
Paul Pogba - (9/10) - Pogba was initially left on the bench by Mourinho with the aim of giving the likes of Lingard more minutes on the pitch. On the hour mark, the Frenchman entered the game in place of Lingard. The substitution paid off for Mourinho as the Frenchman assisted Ibrahimovic's match-winner with a sublime over-the-top through ball.
Juan Mata - (N/A) - The Spaniard came off in the dying minutes of the game in place of Rashford, but didn't do enough to leave an impression with his time on the pitch.