Michy Batshuayi scored deep into added time as Chelseacame from behind to secure a valuable Champions League win against Atletico Madrid.
Despite dominating the Group C clash in the Spanish capital, Chelsea found themselves behind when David Luiz gave away a first-half penalty which Antoine Griezmann converted.
Morata restored parity on the hour mark, though, when he headed home Eden Hazard's cross to equalise before Batshuayi converted from close range with the last kick of the game.
Ahead of the match, Atleti manager Diego Simeone had described playing in the club's new Wanda Metropolitano stadium as like being in a Roman amphitheatre.
Indeed, Los Rojiblancos had won both their league matches in their new arena ahead of hosting Chelsea, and the home fans certainly created an intimidating atmosphere as Atletico started the Group C clash brightly.
But Hazard - making just his second start of the season - showed just how much Chelsea have missed him, exerting his influence as the first half wore on - with his 13th-minute effort taking a deflection and crashing off the post.
Morata, who had scored six Premier League goals in six games including a hat-trick against Stoke on the weekend, then tested Jan Oblak with his header from Luiz's long-range pass which the Atletico goalkeeper tipped over the bar.
The opportunity proved the start of a period of dominance for Conte's men, with the Blues dictating the pace and tempo of the game for much of the first half.
But the visitors soon found themselves trailing needlessly when Luiz's tug on Lucas in the area during a corner kick saw Atletico handed a penalty.
Griezmann, who scored the first-ever goal at the Wanda Metropolitano against Malaga in mid-September, duly converted his spot-kick to give Atletico the lead they hadn't looked like getting.
The hosts could have then doubled their advantage seconds before the break when Koke drove a low effort from 25 yards out which Courtois saved.
The Belgian could, however, only push the ball back out to Saul Niguez whose resulting shot then flew wide.
With the Blues trailing, Conte sent his Chelsea side out from the break looking for the equaliser - which they got in the 60th minute.
Hazard sent a superb cross into the box from the left, which Morata headed past Oblak to restore parity as the man who he replaced, Diego Costa, watched on from the stands following his move from Chelsea to Atletico on Tuesday.
Chelsea kept up the pressure and should have taken the lead when Morata powered into the area but then poked his shot wide of the far corner.
Both managers made a host of substitutions and it appeared as though the game would end 1-1 before late substitute Michy Batshayi won the game at the death.
Chelsea won a late free kick and pushed up field through Marcos Alonso before the left-back cut the ball back forBatshuayi to convert from close range, sending Conte wild on the touchline, and securing a deserved win.
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