Goals from Peter Crouch, Fernando Torres and Steven Gerrard lifted the Reds up to fifth in the Premier League table and improved their prospects of clinching a top-four finish.
Benitez made five changes to the side which lost at West Ham United in midweek but Liverpool seemed devoid of creativity and confidence in a woeful opening 45 minutes.
From the first kick of the game, the visitors seemed determined to pack their defence and hold on for a point and, in the end, that proved to be their downfall.
The Black Cats suffered an early blow when former Manchester United star Kieran Richardson had to be substituted after picking up a knee problem.
Liverpool failed to capitalise on their good fortune though as they struggled to come to terms with the visitors' negative tactics.
The only decent chance of the first half came in the 38th minute when Jermaine Pennant beat Daryl Murphy and crossed for Fernando Torres to head straight at Craig Gordon.
Matters improved after the interval and the Reds finally took the lead when Peter Crouch headed Jamie Carragher's cross past Gordon in the 56th minute.
The goal seemed to raise Liverpool's confidence levels and they added a second goal 12 minutes later when Torres latched on to Crouch's flick and drilled his shot past former Hearts keeper Gordon.
Sunderland thought they should have had a penalty with 17 minutes left when Carragher appeared to block Daryl Murphy's shot with an arm, only for referee Rob Styles to wave play on.
However, with only two minutes left the official awarded Liverpool a penalty when Pennant was upended by Nyron Nosworthy and Gerrard converted the spot-kick.