Jurgen Klopp's title hopefuls had been knocked off the summit by Manchester City in midweek and went into today's match off the back of successive draws and a couple of nervy performances.
It could have been more for Liverpool too, but they settled with for in the end to take back top spot, at least until Man City host Chelsea at the Etihad Stadium on Sunday afternoon.
Liverpool fans may have been fearing another nervy afternoon when Bournemouth made a bright start to the match, and Alisson Becker was called into action inside the opening two minutes to deny Ryan Fraser.
The hosts soon took complete control of the contest, though, and Salah came close twice in quick succession when he first curled an effort over the bar before drawing a routine stop from Artur Boruc moments later.
There was a sense of inevitability about Liverpool's opener when it did arrive midway through the first half, although as was the case against West Ham United, there was again controversy surrounding a possible offside.
Mane appeared to be leaning beyond the last man when James Milner's cross arrived from the right, and the in-form winger got in front of his marker to nod home for his fourth goal in as many Premier League games.
The hosts could have added a second four minutes later when they found themselves with a two-on-one situation, but Wijnaldum's pass to Salah was too heavy and the Egyptian completely missed his kick with an attempted first-time finish.
Roberto Firmino was the next to threaten shortly after the half-hour mark when he was released by an incisive aerial pass from Joel Matip, but his first touch was a fraction too heavy and Boruc was able to smother the ball before the Brazilian could finish.
Liverpool's second did arrive moments later, though, as Andrew Robertson picked out the forward run of Wijnaldum, who took the ball down inside the area before lifting an exquisite volleyed lob over Boruc and into the net.
Salah almost rivalled that moment of individual magic shortly before half time when he collected the ball on the edge of the area before flicking it up for himself and unleashing a volley towards goal which forced Boruc into a flying save.
Wijnaldum drew another stop from the busy Bournemouth keeper before the interval, while Jefferson Lerma flashed a long-range shot off target moments later as Bournemouth made a rare foray forward with just seconds left of the first half.
The Cherries may have felt relieved to reach the break with only a two-goal deficit, but they were three behind within two minutes of the restart as Liverpool made a perfect start to the second half with a devastating team goal.
Naby Keita's lofted ball sent Firmino through on goal, but instead of shooting the Brazilian instead produced an impudent backheel for Salah, who kept his composure to tuck his finish into the bottom corner.
At that stage it looked like being a case of how many Liverpool would end up scoring, and they almost added a fourth just before the hour mark when Wijnaldum's clipped cross found Mane unmarked at the back post, only for the winger to nod wide when he should have done better.
It was the first of a plethora of chances for Liverpool to extend their advantage which went begging, and none came closer than Salah's 76th-minute strike as the Egyptian was only denied his 50th Premier League goal for Liverpool by the crossbar following some slick link-up play with Firmino.
Bournemouth offered precious little to disrupt Liverpool's dominance throughout the second half, although substitute Lys Mousset did provide a couple of relative highlights for the visitors following his introduction, flashing an audacious strike wide with his first touch and then forcing a save from Alisson with a powerful drive from a tight angle.
In truth, the hosts looked like the only team that would add to the scoring, though, and Keita was the next to squander a clear chance when he blazed over after the ball had fallen kindly for him inside the area.
A blistering counter-attack with three minutes of normal time remaining should have provided the fourth goal with Firmino clean through, but his finish was tame and Boruc came out on top in the one-on-one duel after Firmino had opted to ignore Salah and Virgil van Dijk in support.
Despite being beaten three times, Boruc was largely responsible for keeping the scoreline down, and he made one final big save late on to deny Trent Alexander-Arnold, who was thwarted from close range on his return from almost a month out with a knee injury.
It was still a convincing defeat for the visitors, though, as they became the first team since Portsmouth in February 2006 to lose eight successive Premier League away games while conceding at least twice in each game, while it is the first time they have suffered that many consecutive losses on the road as a club since 1984.
Liverpool, meanwhile, are now unbeaten in 34 home league games and seize top spot back from Man City, who need to beat Chelsea on Sunday to leapfrog the Reds again - although Liverpool would then have a game in hand over the champions.
LIVERPOOL (4-3-3): Alisson; Milner, Matip, Van Dijk, Robertson; Wijnaldum (Alexander-Arnold 77'), Fabinho, Keita; Salah, Firmino (Sturridge 90'), Mane (Origi 87')
BOURNEMOUTH (4-5-1): Boruc; Smith, S Cook, Ake, Rico (Mepham 80'); Ibe (Solanke 59'), Gosling, Lerma (Mousset 73'), Surman, Fraser; King