Reds boss Hodgson was under pressure after Liverpool's nightmare start to his reign, with the team languishing in the relegation zone amid talk of dressing room unrest.
But the win over Hodgson's former club Blackburn brought some much needed relief to the beleaguered former Fulham chief.
Fernando Torres claimed the winner in a second-half spell which brought three goals in the space of five frantic minutes.
But Torres came to the rescue with only his second goal of the season to ease the tension in the red half of Merseyside.
With new co-owner John W Henry absent through sickness, the American sent David Ginsberg and Michael Gordon to see if Liverpool could end their worst start to a top-flight campaign for more than half a century.
Torres, who has looked off-form in recent weeks, was immediately involved in the game's opening opportunity in the eighth minute.
It didn't deter Liverpool though and Kyrgiakos was next test Robinson, forcing the Rovers goalkeeper to palm the Greek defender's out following Steven Gerrard's corner.
On the half hour mark it was the turn of Gerrard to be frustrated by his old England team-mate Robinson.
A sweeping move allowed Gerrard to canter forward but his 20-yard drive, not for the first time, was kept out by the Rovers stopper.
Meireles' 25-yard strike was destined for the corner but struck Michel Salgado on his face.
But Liverpool weren't helping themselves, with Maxi following Lucas in missing close-range chances on the stroke of half-time.
The nerves and tension enveloping Anfield were finally released as the game sparked into life after the break with three goals in five minutes.
Gerrard's corner was met by a thumping header from Kyrgiakos that beat Rovers defender Martin Olsson on the line in the 48th minute.
But the joy among the home fans was shortlived as a comical own goal handed Blackburn a leveller they barely deserved three minutes later.
But within two minutes Torres had scored only his second goal of the season - and the first since August - to end a barren run in front of goal.
Cole provided the cross from the left and Torres ghosted in unmarked at the back post to volley home.
Liverpool were happy to sit back having regained their lead so soon. It meant the chances dried up for the Reds as Blackburn found a foothold on proceedings.
But the visitors never looked like playing on Liverpool's nerves as their winless streak at Anfield stretched to 17 years.
Source: AFP Global Edition