Depsite being under the quash in the opening periods Chelsea arguably had the best chances of the first-half with Eden Hazard hitting the post and Álvaro Morata testing Jan Oblak, but still found themselves behind as Antoine Griezmann converted his penalty in the 40th minute.
Morata took his chance the second time around as he got The Blues' equaliser just before the hour mark, it looked like both sides would have to settle for a point as the contest entered its dying embers but Batshuayi tapped home three minutes into extra-time to secure a crucial victory for Antonio Conte's men.
Trying to test them on their own soil
After their 6-0 demolition of Qarabag FK this would be Chelsea's first test on their return to Europe's elite competition and certainly were tested early inside the Wanda Metropolitano, but as the early minutes rolled by Conte's men began to come into the contest.
The first big chance fell to the visitors as Hazard managed to find space 30 yards out and move forward, the Belgian hit a sweet effort which had Oblak well beaten but it cannoned back off the post.
They came forward again in the 24th minute as David Luiz pinged an excellent 40-yard box towards the back-post, Morata was lurking waiting for his chance and got his head on it but the first-time effort was tipped over the crossbar by Oblak.
Mistake proves costly
Despite their dominance Diego Simeone's side never really had a clear-cut chance to show for their efforts as the half entered it's final five minutes, but were given a golden opportunity to change all that when they were handed a penalty.
The blame lands at the door of Luiz who lazily pulled on the shirt of former Blue Filipe Luís and it was easy enough for referee Cüneyt Çakır to point to the spot, Griezmann stepped up and made no mistake as he rifled it into the roof of Thibaut Courtois' net.
Simeone will have been left scratching his head to how it wasn't two almost instantly, Koke hit a low effort which caused Courtois to push the effort back into the feet of Saul but he somehow managed to put it wide from ten yards out.
Pulling his side back into it
Chelsea came out for the second period knowing that they would need one of their star men to step up and pull them out of their self-made mess, Morata once again showed he was the right man to bring in to Stamford Bridge as he leveled things up.
Luiz gained some redemption starting the move by spreading the play out to Hazard, the Belgian played in a great ball into the near-post where the striker was waiting to faintly flick it beyond Oblak.
Hazard was at it again three minutes later as he did brilliantly to bomb down the right-hand side to keep the move alive, he put in a low ball to the six-yard area where
Cesc Fàbregas was waiting but the midfielder's brain seemingly went blank as he couldn't sort out his feet and managed to poke it wide.
Snatching it with the last kick
Both sides continued to push each other to their limits right to the death to see if either would crack, and on this occasion it was The Blues who came out victorious as they won the contest with the final kick of the game.
Despite the seconds ticking down Chelsea played a very calm game on the edge of the Atlético area before Tiémoué Bakayoko flicked it into Marcos Alonso, the Spaniard pinged it into the mixer to find Batshuayi who rolled it home from three yards.