Jurgen Klopp's side were growing anxious after Darwin Nunez's early opener was cancelled out by Conor Bradley's own goal in the second half. But Mac Allister eased the nerves around Anfield with a brilliant finish from the edge of the area and Cody Gakpo sealed the points in the closing moments.
On a potentially pivotal evening in the title race, Liverpool moved two points clear of second placed Arsenal with eight games left for each of the three teams involved in a gripping battle for supremacy.
Arsenal's 2-0 win against Luton had knocked Liverpool out of pole position on Wednesday, with third-placed Manchester City's 4-1 rout of Aston Villa keeping them in the hunt.
But Liverpool, unbeaten in their last 28 home league matches, are now a step closer to being crowned English champions for a record-equalling 20th time and first since 2020.
Klopp's treble chasers have already won the League Cup and face Atalanta in the Europa League quarter-finals as they eye a memorable farewell for the German in his last season. However, they will have to improve on this erratic display to hold off Arsenal and champions City, who are three points adrift of Liverpool.
Liverpool head to Manchester United in the league on Sunday for a crucial clash with their bitter rivals. The Reds had to come from behind to beat Brighton last weekend, but Klopp insisted he was feeling "calm" as the title race approaches a dramatic climax.
Even so, his heart must have been beating a little faster than usual when United almost snatched a shock lead. Jack Robinson's long throw reached the unmarked James McAtee in the area and on-loan Manchester City youngster's volley forced a reflex save from Caoimhin Kelleher.
From the resulting corner, Ben Brereton Diaz almost
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