Costa, whose return to Atletico was completed on Tuesday, watched on as Chelsea responded from David Luiz’s needless concession of a penalty scored by Antoine Griezmann.
Former Real Madrid striker Morata headed in Eden Hazard’s cross for his seventh goal in eight games for Chelsea, before Batshuayi struck with the final kick of the game.
The dramatic finish gave the Blues two wins from two Champions League Group C games.
It was no less than Antonio Conte’s visitors deserved after a strong showing, with Tiemoue Bakayoko, N’Golo Kante, Morata, and Hazard particularly impressive.
Chelsea beat Qarabag 6-0 in the opening round and next play Roma in a double-header.
“We are very happy. It was a tough game against one of the biggest teams in Europe,” Hazard said. “We deserved to win the game. It was not easy today but we did it.”
This was the trickiest of Chelsea’s group games as Atletico played in Europe at their new Estadio Metropolitano home for the first time.
And Los Rojiblancos, who had won 30 of their last 36 European games at the Vicente Calderon stadium, losing just twice, suffered their first home defeat to English opposition.
Only one former Chelsea player was in Atletico’s starting line-up, Filipe Luis, with Fernando Torres on the substitutes’ bench.
Costa watched from the stands after returning “home”.
Chelsea goalkeeper Thibaut Courtois spent three years on loan at Atletico, winning La Liga in 2014 and reaching the Champions League final at parent club Chelsea’s expense. Courtois’ Belgian compatriot Hazard attempted to ignite Chelsea’s attack, taking heed of Conte’s pre-match encouragement to take his game to the next level.
The playmaker first ran at Atletico and found Morata, who dragged a shot wide across goal.
Morata went close from Luiz’s cross, but his header was straight at Jan Oblak.
A combination of Luiz and Gary Cahill cleared Juanfran’s cross towards Griezmann, who had hardly had a kick until presented with a spot-kick by Luiz.
Yannick Carrasco’s shot was blocked for a corner from which Luiz, using his left arm which was strapped to protect his fractured wrist, hauled over Hernandez. Griezmann converted the penalty.
It should have been 2-0 at the interval.
Courtois parried Koke’s shot straight to Angel Correa, who side-footed wide.
Chelsea equalised after 60 minutes when Hazard crossed right-footed from the left and Morata netted with a precise glancing header.
It was his first goal in seven games against Atletico as he became the first opposition player to score at their new home.
Chelsea soon came close to a second. Fabregas prodded a Hazard cross wide when stretching to meet the ball before Kante shot wide.
Morata spurned a difficult one-on-one chance as Oblak forced him wide.
But Chelsea’s persistence paid off when Batshuayi, on for Morata, tucked in Marcos Alonso’s cross.
Oblak, Juanfran, Godin, Lucas, Filipe Luis,Koke, Thomas (Gimenez 77), Saul,Carrasco (Torres 69), Griezmann, Correa (Gaitan 70).
Courtois, Azpilicueta, Luiz, Cahill, Moses, Kante, Bakayoko, Alonso, Fabregas (Christensen 85), Hazard (Willian 82), Morata (Batshuayi 81).
Cuneyt Cakir (Turkey).