Centre-back Ragnar Klavan was Liverpool's unlikely match-winner at Burnley as his close-range header in the fourth minute of added time made light of the absence of three of the "Fab Four."
Nahki Wells replaced Scott Arfield in the 86th minute.
With £75 million world-record defender Virgil van Dijk waiting in the wings for his debut, the focus has been turned on the Reds' central defenders, but it was at the other end of the pitch where Estonian Klavan proved his worth.
Jurgen Klopp's side looked like they had thrown away two points when Johan Berg Gudmundsson's 88th-minute equalizer cancelled out a stunning strike from Sadio Mane.
However, Klavan popped up barely a yard out to nod in from a free kick move to secure a hard-fought 2-1 win.
Kane Hemmings scored twice as Mansfield stormed into the Sky Bet League Two play-off places courtesy of a 3-1 home win over Reggie Lambe and his Carlisle United teammates.
Hemmings's two goals was sandwiched by a Rhys Bennett effort to continue the Stags' fine form which has seen them lose only once in 18 games.
Carlisle had pulled a goal back through Jamie Devitt's penalty but they missed the chance to close the gap on the top seven.
The visitors might have gone ahead in the seventh minute when an unmarked Tom Miller sidefooted wide from seven yards from Danny Grainger's long cross.
That proved crucial as within two minutes Mansfield were ahead as Hemmings latched onto Grainger's poor backpass to sidestep the goalkeeper and slot in from a narrow angle.
It was 2-0 on the half hour when Lee Angol met CJ Hamilton's cross to force Jack Bonham to save under the cross bar, but the keeper was helpless as Rhys Bennett turned the dropping ball in from close range.
United were back in it in the 67th minute through a Devitt spot-kick after keeper Conrad Logan had felled substitute Richie Bennett.
Then Sam Cosgrove and Richie Bennett somehow hit the woodwork in succession from Hallam Hope's 73rd-minute cross.
They were made to pay two minutes later as Hemmings turned home a low Alfie Potter cross from close range.