But Suarez's header only served to paper over the cracks of another faltering Liverpool performance.
The Reds went into the game on the back of six losses in seven matches, their worst sequence for almost 60 years, and with criticism mounting on both the players and manager Kenny Dalglish.
Fragile confidence was eroded further when Chris Herd put the visitors ahead early on but a much-needed win for the Midlanders, for whom relegation worries have been growing, proved beyond them.
While a month ago Dalglish argued, with some justification, that results were not reflecting performances that has not been the case in the last few weeks.
Since the turn of the year they have won just twice in the league, taking nine points from 13 games as their bid for a top-four place evaporated in the euphoria of February's Carling Cup triumph.
Defeats to the likes of Wigan at home and a late capitulation at QPR destroyed any confidence the squad had and undoubtedly impacted on their form.
Their anxiety and uncertainty was not helped by goalkeeper Doni, who had previously played only 57 minutes of an October friendly against Rangers, having to make his debut in place of the suspended Jose Reina - ending a run of 183 successive league appearances.
The Brazilian failed his first test and it proved expensive as he flapped at former Liverpool defender Stephen Warnock's left-wing cross in the 10th minute, allowing Barry Bannan to cut the ball back for the unmarked Herd to bend in a shot.
However, Liverpool would have been ahead by then had it not been for the reactions of the experienced Shay Given who clawed Dirk Kuyt's shot off the line after Stewart Downing's low cross picked out the Holland international at the far post.
The home side's response to going behind was slow as despite a succession of corners Martin Skrtel's header wide of the post was the closest they came.
Suarez had a valid claim for a penalty turned down when he was caught by Alan Hutton but it was not until the final minute of the half the Reds really posed a threat.
The best chance fell to Kuyt from Steven Gerrard's cross-shot but the Dutchman ballooned over from five yards before Suarez fired straight at Given.
Dalglish switched to 4-4-2 for the second half with Gerrard playing wide right and the captain almost helped deliver the equaliser.
His 53rd-minute cross picked out Suarez whose header beat Given but bounced off the far post, although it still needed the goalkeeper's quick reactions to flick the ball away from an almost impossible position behind him to prevent it crossing the line.
Villa, content to hang on to their lead, were starting to come under more sustained pressure and the Liverpool manager attempted to turn the screw by sending on Andy Carroll and Craig Bellamy, effectively playing with four forwards.
But still they struggled to test Given with Bellamy, given time to bring the ball down on the left of the penalty area, driving against the outside of the post.
The woodwork was struck again in the 82nd minute but this time it actually benefited Liverpool.
Gerrard's cross from the right saw substitute Daniel Agger, on for Jose Enrique, plant a header against the underside of the bar but when the ball bounced down Suarez was on hand to nod in from close range.
Carroll headed straight at Given from another Gerrard cross before the captain's swerving shot was kept out by the goalkeeper's legs in added time.
A victory would have flattered the home side who, despite making all the running after going behind, were far from impressive and made hard work of getting a point against a side who had won just twice in 11 games.