An aberration from Ajax goalkeeper Andre Onana gifted Curtis Jones his first Champions League goal and handed Liverpool qualification to the last 16 as Group D winners with a 1-0 victory at Anfield.
The focus had been all been on Irish goalkeeper Caoimhin Kelleher making his competition debut between the posts for Jurgen Klopp's side because of injury to Alisson Becker but the 22-year-old did not put a foot wrong.
Instead the spotlight fell on Onana, making his 23rd Champions League appearance, who inexplicably pulled out of claiming Neco Williams' inswinging cross and Jones nipped in behind him to score the decisive goal just before the hour.
Liverpool needed only a draw from the fixture to secure progress to the knockout stage but Midtjylland getting a point against Atalanta guaranteed top spot, rendering next week's trip to Denmark a dead rubber and giving Klopp some much-needed breathing room to rest some of his players.
CHAMPIONS LEAGUE: GROUP STANDINGS
Alisson is likely to be out for up to 10 days with a hamstring problem sustained at Brighton on Saturday, taking the injury count up to nine.
Klopp opted to play Kelleher, who had only four domestic cup appearances to his name, instead of established number two Adrian and was not disappointed as the Republic of Ireland Under-21 international produced several good saves, the best late on from experienced goalscorer Klaas Jan Huntelaar's close-range header.
Jones had started brightly for the hosts, drawing Onana's first save of the game and then hitting the post from Mohamed Salah's lay-off with the goalkeeper beaten.
Sadio Mane wanted a penalty when he went down in a Perr Schuurs-Noussair Mazraoui sandwich but referee Tobias Stieler was not interested.
After their early thrusts the game opened out with Ajax's fluid system, which was often 2-4-4 with Schuurs and former Manchester United defender Daley Blind left alone to deal with Mane and Salah.
Key to the visitors' game-plan was getting ex-Everton midfielder Davy Klaassen into an advanced position between centre-backs Joel Matip and Fabinho, a tactic which created its fair share of issues.
Klaassen forced Kelleher into his first save low down with a header, which ultimately was flagged offside, and was inches away from connecting with Dusan Tadic's deflected cross as the Liverpool defence struggled with his late runs into the box.
Kelleher tipped over Mazraoui's shot from distance to further boost his confidence as the game continued to open out, with Schuurs booked for tripping Mane as he threatened to race through the inside-right channel just before the break.
Klaassen remained a cause for concern in the second half, heading wide when he should have hit the target, while David Neres hit the post after Kelleher had done well to parry Mazrouai's low shot.
But despite continuing to lose out in the possession stakes Liverpool took their chance when it came. Or rather when it was dished up on a plate.
Captain Jordan Henderson, who had spent the whole game guiding and cajoling Williams, cut the ball back to the young defender, who switched it onto his weaker left foot and sent over a deep cross.
Onana came for it and then left it, assuming it was drifting out of play. He had not counted on Jones stealing in beyond the far post to squeeze a shot home from a narrow angle.
It was the first time two teenagers had combined for a Liverpool goal in the Champions League and with his current injury crisis Klopp will hope it is not the last.
Onana tipped substitute Roberto Firmino's shot onto a post but the damage had already been done and Kelleher showed him how it should be done with his point-blank save from Huntelaar.