Maxi Rodriguez toe-poked an 86th-minute winner as Liverpool won at Bolton to move out of the relegation zone.
Fernando Torres missed two first-half chances to open the scoring, while Steven Gerrard shot wide and Bolton's Stuart Holden had a volley well saved.
Liverpool lost Joe Cole to a hamstring injury but responded well with Sotirios Kyrgiakos and Maxi both going close.
Bolton pushed for a winner but it was Liverpool who got it, Maxi prodding home after a sublime flick from Torres.
The result - Liverpool's first away victory since they won at Burnley in April - sees Liverpool jump from 18th to 12th in the table.
Roy Hodgson's men are now just three points behind fifth-place Tottenham and five adrift of Manchester City in fourth.
And it is a triumph that will fill them with confidence ahead of Thursday's Europa League meeting with Napoli, which precedes the visit of Chelsea on Sunday.
Bolton will feel hard done by after a performance full of energy and ambition, but they were ultimately punished for a lack of cutting edge in the final third.
Liverpool knew a point would be enough to lift them above the bottom three and Hodgson opted to name an unchanged side to the one which beat Blackburn last time out.
That meant Torres was deployed as the lone striker with Gerrard, Maxi and Cole in support - and the foursome looked dangerous from the outset.
Hodgson had not overseen an away league victory since the opening day of the 2009-10 season - when he was Fulham manager - but his team were full of attacking intent and they dominated the early exchanges.
Eight of Liverpool's previous nine league goals had been scored or created by Gerrard or Torres and the pair almost continued that sequence when Torres rose highest to meet Gerrard's corner but directed his header over the bar.
When the pair combined again a few minutes later, Liverpool should have taken the lead. A delicious lay-off from Gerrard sent Torres scurrying clear, but the Spaniard tried to turn inside Gary Cahill and a poor touch enabled the defender and his goalkeeper Jussi Jaaskelainen to avert the danger.
Liverpool were getting forward in numbers and a couple of crosses from left-back Paul Konchesky troubled the Bolton defence before Jaaskelainen reacted quickly to race off his line and prevent Torres latching on to Maxi's through-ball.
Bolton managed to emerge from that spell of pressure unscathed and soon began passing and moving with the confidence of a side who came into the match unbeaten at home this season.
One particularly eye-catching move saw Holden meet Kevin Davies's flick with a sweetly-struck volley that startled Liverpool keeper Pepe Reina.
The hosts wanted a penalty after for a challenge on Chung-Yong Lee by Jamie Carragher, and they were appealing again when Paul Robinson's left-wing cross appeared to brush the same defender's arm.
Liverpool finished the half on top, Gerrard shooting wide from a promising position after being teed up by Maxi, but it was Bolton who made the more sprightly start to the second period.
Unfortunately for Owen Coyle's men, Liverpool were able to comfortably repel everything the Trotters threw at them.
The momentum briefly swung back in Liverpool's direction but, similarly, they struggled to carve out significant chances and suffered a set-back when Cole was forced off through injury.
He was replaced by striker David Ngog and the Frenchman's arrival - prompting Liverpool to switch from 4-2-3-1 to 4-2-2-2 - seemed to benefit the Reds.
Kyrgiakos glanced a header just over from Gerrard's corner and Maxi's overhead volley was narrowly too high after a Gerrard cross and Torres knockdown.
Back came Bolton and they saw another penalty shout rejected when Kyrgiakos appeared to shove Davies to the ground before Reina saved well to deny Johan Elmander and Zat Knight headed over from Matthew Taylor's corner.
But after Elmander flashed a strike wide and Davies narrowly failed to connect with Holden's inviting free-kick, Liverpool struck.
Lucas Leiva collected possession on the left and fed the ball into Torres, who flicked it through the legs of a Bolton defender to release Maxi. The Argentine's strike was far from clean but he did enough to beat Jaaskelainen and seal a vital three points.