Michy Batshuayi climbed off the bench to fire the Blues to a memorable victory in Amsterdam.
The Belgian striker made amends for a shocking earlier miss four minutes from time to hand last season’s semi-finalists their first defeat of this campaign.
The Blues rode their luck at times, not least when an Ajax goal was ruled out by VAR for the tightest of offside calls, and when the hosts hit the frame of the goal.
But Lampard’s young side grew in stature as a frantic, tetchy encounter wore on and ran out deserved winners when Batshuayi rifled in off the underside of the crossbar.
“The subs were second to none,” he said. “Sometimes the hardest thing is leaving someone out. But it’s great for the spirit of the squad when subs come on and have an impact like that.
“I was frustrated when Michy missed, and whatever had happened after that I would have been proud, but I know Michy can finish.
“Christian’s assist is as important as the finish, and the fact the sub scored makes me so happy.”
The memory of a visit from a London club remains raw for Ajax following Tottenham’s last-gasp semi-final comeback in May, and this was another painful experience for their youthful outfit.
It could have been different had VAR not spotted that Quincy Promes, or at least a microscopic part of him, was offside before he slid the ball home in the first half, while Edson Alvarez grazed a post in the second period.
Captain Dusan Tadic said: “I think it was 50-50. Chelsea are a good club, but we can do better.
“We were sloppy and made easy mistakes. Now we have to focus again on the next game.”