Wigan Athletic 1 Liverpool 0
The visitors threatened early on at the DW Stadium as Steven Gerrard and Fernando Torres both wasted chances, before Rodallega fired past Pepe Reina ten minutes before the break.
Liverpool's Sotirios Kyrgiakos scrambled Marcelo Moreno's goal-bound block off the line in the second half before Torres spurned a glorious chance to level as Wigan hung on for their first victory over the Reds.
The hosts began the game just a point clear of the drop zone after going seven games without a win, while the Reds had revived their hopes of finishing in the top four after taking ten points from their past five games.
Gerrard fired an early warning shot across the Wigan bows when he smashed a rebound from Javier Mascherano's strike over the bar.
Torres should have put Liverpool ahead in the eighth minute when he struck the post after collecting Maxi Rodriguez's header inside the penalty box.
But after weathering the storm the Latics began to assert themselves and Charles N'Zogbia lashed a teasing ball across the box, before Rodallega fired a free-kick over and Emiliano Insua was booked for hauling down Frenchman N'Zogbia.
In the 35th minute the home side made the most of their dominant position when Rodallega slipped his eighth goal of the season past Reina.
The Colombian striker continued to threaten the visiting goal after the break and Reina was called on twice in quick succession to deny him.
And it was Wigan who almost doubled their advantage on the hour mark when Moreno blocked Jamie Carragher's header and - with Reina stranded - Kyrgiakos was forced to head off the line.
Reina smothered N'Zogbia's 73rd minute strike before Dirk Kuyt headed the ball down to Torres eight yards out, but he blazed his volley wide.