Chelsea lost their first game of the campaign at home to Valencia but have now bounced back with successive away victories over Lille and last season’s semi-finalists.
Ajax remain top of the group on six points while Chelsea have climbed to second position with Lille and Valencia squaring off later.
The visitors carved the hosts’ defence open in the 14th minute with a neat one-two involving Tammy Abraham and Mason Mount that ended up with latter’s low shot being kept out by goalkeeper Andre Onana.
Ajax misplaced a defensive header in their own half in the 27th minute but Callum Hudson-Odoi could not take full advantage, slicing his effort wide from ten yards out.
Ajax thought they had taken the lead in the 35th minute when Quincy Promes stabbed home Hakim Ziyech’s deflected strike but VAR intervened in Chelsea’s favour and ruled the goal out for offside.
After the break Ajax came close to opening the scoring but Edson Alvarez’s 59th minute header from a corner hit the post and bounced out of play.
Michy Batshuayi replaced Abraham and Chelsea’s best chance fell the way of the Belgian shortly after, but he scooped his shot horribly over when clean on goal from a deflected Christian Pulisic shot.
Batshuayi however made amends with five minutes to go as he riffled Pulisic’s cut-back in off the underside of the Ajax bar to give Chelsea all three points.