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.
“I’m delighted with every element of the performance,” said the Blues boss.
“It feels huge – it’s just six points in the group and we play Burnley on Saturday. But I think we’re allowed to be excited tonight.
“That’s the blueprint. There are no excuses for us now. That’s the standard and we can’t drop it.
“The young players are still babies in terms of Champions League minutes so this was a huge test for them.
“There was a good balance of young players and experience. We need to realise the things that made that happened tonight because Ajax are a top, top team.”
Liverpool midfielder Alex Oxlade-Chamberlain announced his return to the Champions League after an 18-month absence with two goals in a 4-1 win in Genk.
The England international missed all but 20 minutes of last season with a serious knee injury sustained in the semi-final win over Roma in this competition in April 2018.
He made up for lost time by producing exactly the sort of performance manager Jurgen Klopp expects from him, driving forward from midfield and – more importantly – scoring.
His first was good, firing home from just outside the penalty area, but his second was sublime, flicking a first-time shot in off the crossbar.
Sadio Mane and Mohamed Salah also scored – Stephen Odey grabbed a late consolation for the hosts – as Liverpool recorded their first away win in the group stage in five matches and only their second in 10.
Oxlade-Chamberlain said : “I’ve definitely missed it. It’s nice to be back out there. It’s a special tournament to play in and a competition we all want to grow up and play in one day.”