The result must have been especially pleasing for the Latics boss because he was without Antonio Valencia (hamstring), Chris Kirkland (back) and Titus Bramble (suspended), while it was Wigan's first game since the sale of Wilson Palacios and Emile Heskey.
But the result is another blow to Liverpool's title ambitions.
Rafael Benitez's team have now drawn their last three league games and missed out on the chance to move level on points with leaders Manchester United.
Chelsea move above Liverpool in the table and Benitez's team are still waiting for their first Premier League win of the year.
The tension was clear to see on the face of Benitez, with the Reds boss seemingly unable to remain in his seat for more than a few seconds at a time before springing up and barking instructions from his technical area.
Benitez frustrated by 'crazy' game
His team had virtually monopolised possession in the opening stages but did not really threaten Mike Pollitt's goal until Torres came within inches of an opener.
The Spain striker got across Boyce and flicked Steven Gerrard's left-wing cross towards goal but was denied by the far post.
The visiting team created several other first-half openings, with Torres heading wide and 36-year-old Pollitt making a decent save to deny Ryan Babel.
Pollitt later looked to have done enough to prevent Benayoun from scoring after forcing the Israel international wide but the Liverpool player smashed the ball home from the most acute of angles.
The ball skimmed the post on its way into goal and it was an especially brilliant strike given that Benayoun, who scored the winner at the JJB Stadium last season, had to shoot on the turn while trying to keep his balance.
Referee Phil Dowd, who earlier waved away penalty appeals for a handball against Martin Skrtel, played his part in the goal by playing an intelligent advantage after a foul on Gerrard.
Gerrard almost doubled Liverpool's lead on the stroke of half-time with a free-kick from an outrageous distance that narrowly missed.
Wigan, fielding a new-look all-Egyptian strikeforce of Amr Zaki and Mido, did have a period of pressure midway through the half and really should have taken the lead.
Bruce praises terrific performance
Boyce was left completely unmarked as the Liverpool defence tried to play him offside from Daniel de Ridder's cross but the defender headed wide from 12 yards.
Wigan tried to force the pace after the break while the Reds pressed and probed as they looked for a decisive second.
Benayoun dribbled brilliantly into the Wigan box but his pass across goal was blocked, while Gerrard shot across goal but wide of the target.
Torres made way for Albert Riera and Kuyt came on for Benayoun but it was Wigan who scored next after Lucas fouled Koumas with little sign of immediate danger to the Liverpool goal.
Robbie Keane, who had been named on the bench, replaced Gerrard within seconds of Wigan scoring but there were to be no further chances for Liverpool to snatch victory.
Wigan: Pollitt, Melchiot, Boyce, Scharner, Figueroa, De Ridder (Koumas 63), Brown, Cattermole, Taylor (Camara 80), Zaki (Rodallega 77), Mido. Subs Not Used: Kingson, Edman, Watson, Kapo.
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