Antonio Conte's Premier League champions were unfortunate to be behind when Antoine Griezmann scored Atleti's first European goal at their new home from the penalty spot.
The opener from the man Costa will join in a dream forward line from January onwards, having finalised his Atletico return from Chelsea on Tuesday, arrived five minutes before half-time but Alvaro Morata gave another indication that Conte's side will cope perfectly well without their old talisman.
Morata nodded in a 59th-minute cross from the exceptional Eden Hazard to move on to seven goals in all competitions this season and worse was to follow for Diego Simeone's men.
Instead of launching a free-kick into the area as the allotted period of injury time expired, Chelsea calmly worked possession around, with Marcos Alonso picking out substitute Batshuayi for a simple finish that left the watching Costa ashen faced.
Chelsea are top of the standings after back-to-back wins, two points clear of Roma, while Atleti have ground to make up in their pending double-header against Qarabag.
Conte handed a start to the fit-again Hazard and Chelsea's influential playmaker began brightly.
Hazard embarked upon a driving run in the fifth minute, sliding through a pass for Morata to drag wide, before cleverly cutting in from the left to fire into the side netting.
Morata was off target once more from a similar position to the right of goal inside the Atletico penalty area, provoking an animated response from Conte on the touchline.
Chelsea's 3-5-2 was causing Atleti persistent problems and the jewel in the formation, Hazard, engineered space 25 yards out in the 13th minute to unleash a vicious swerving drive against the post, with home goalkeeper Jan Oblak rooted to the spot.
Oblak was a necessarily more active participant after the first half ticked past midway and Morata's header from David Luiz's raking pass forced him to tip over.
Atletico belatedly steadied themselves and took the lead having been on the back foot.
Luiz needlessly grabbed Lucas Hernandez's shirt as the defender looked to attack a near-post corner and Griezmann outfoxed Thibaut Courtois by sending his spot kick down the middle.
It was almost 2-0 on the stroke of half-time when Courtois parried Koke's low drive dangerously into the path of Saul Niguez, who sidefooted narrowly wide.
Saul got above Tiemoue Bakayoko to head past the post from a Koke set-piece early in the second half, while a wicked cross from Cesar Azpilicueta flashed agonisingly between Morata and the face of goal at the other end.
It was no surprise when Hazard served as the architect of the away side's equaliser, curling in a sumptuous ball from the left and obliging Morata to nod home.
Uncharacteristic panic suddenly gripped the Atleti defence and after a clutch of red-and-white shirts scurried towards Hazard in vain, an unmarked but stumbling Cesc Fabregas was unable to turn in the cutback from close range.
Morata's outing should really have proved more profitable than it was.
The Spain striker streaked away from Lucas in the 75th minute only to misjudge a tame effort, but Batshuayi - on for Morata - clinched the points with a close-range finish deep in injury time.
Key Opta facts:
- Chelsea are first side to win away in the Champions League against Atletico Madrid in the Spaniards’ last 12 games in the competition on home soil (since losing to Benfica in September 2015).
- Chelsea are also only the fourth side to score away to Atletico in Europe in the Spanish giants’ last 20 games on home soil.
- The Blues are now unbeaten in their last 10 Champions League away games against Spanish sides (W3 D7).
- Since the start of 2015-16, Antoine Griezmann has had a hand in 51.5 per cent of Atletico Madrid's 33 CL goals (14 goals, 3 assists)
- Alvaro Morata has scored his first goal against Atletico Madrid in his seventh game against them in all competitions.
- Michy Batshuayi has scored five goals in his last three games for Chelsea in all competitions, as many as in his previous 16.
- In 2017, no player has scored more substitute goals for a Premier League club in all competitions than Michy Batshuayi (4, level with Olivier Giroud).