The Colombia international volleyed home Emmerson Boyce's 35th-minute cross after Dirk Kuyt had needlessly given away possession close to his own penalty area.
Liverpool showed little of the quality required for a place in the Champions League once Fernando Torres had hit a post in the eighth minute and the Latics were well worth their victory.
It was Wigan's first Premier League win over Liverpool and only their second over one of the so-called 'big four' - the other coming at home to Chelsea earlier this season.
That ended a run of seven league matches without a victory and lifted them four points clear of the relegation zone.
And while it was only sixth-placed Liverpool's second defeat in 11 games it could have done irreparable damage to their chances of finishing fourth as they have now played more games than all of their rivals.
Rafael Benitez's side's problems are clear to see as this was the sixth time in their last eight away league matches they have failed to score.
The closest they came in this game was when Torres hit the outside of the upright after Maxi Rodriguez's header from Steven Gerrard's corner dropped to him at the far post.
But Wigan quickly grew in confidence and Marcelo Moreno was only inches from connecting with a driven cross through the six-yard area by Charles N'Zogbia, who was causing left-back Emiliano Insua plenty of problems.
Rodallega curled over a 20-yard free-kick after being fouled by Lucas Leiva while Insua's difficulties against N'Zogbia continued as he was booked for bringing down his opponent in the centre-circle.
Gerrard could have opened the scoring in the 26th minute after good link play between Rodriguez, Kuyt and Yossi Benayoun but the England international's first shot was blocked by Paul Scharner and although he quickly recovered he could not hit the target with the follow-up.
Lucas was next to be booked for tripping Titus Bramble and Sotirios Kyrgiakos was also cautioned for cynically blocking off Scharner.
Liverpool were struggling to find any sort of rhythm and their alarming tendency to give the ball away proved expensive in the 35th minute.
Kuyt, deep position on the left, rolled the ball aimlessly to Boyce who instantly fired a cross to the far post where Rodallega poked home.
It was the first time the Reds had conceded in the opening 45 minutes of a league match for 11 games.
Bramble was then booked for clattering into the back of Torres, who headed over Rodriguez's cross from six yards just before half-time.
Within 42 seconds of the second half kicking-off Mascherano had to be quick to block Rodallega's shot.
At the other end Torres, unusually for him, failed to hit the target from Rodriguez's cut-back.
Ten minutes into the half Johnson replaced Lucas, with Mascherano returning to his favoured central midfield.
Liverpool almost gifted Wigan a second as Jose Reina came out to claim a through-ball only for Carragher to knock it past him and then smashed his clearance into Moreno.
The ball looped towards the goal only for Kyrgiakos to get back to head over his own crossbar.
However, Liverpool were not getting any better and Torres' ambitious 25-yard volley summed things up when it went out for a throw close to the right corner flag.
Wigan should have had a second in the 73rd minute when Rodallega's pass put N'Zogbia through but his shot was partially stopped by Reina and Johnson scrambled the ball out at the far post under pressure from Scharner.
Moments later Torres' volley from Kuyt's header down rolled agonisingly wide of the post.
Liverpool's frustrations boiled over as first the Spain international was booked after chasing Boyce half the length of the pitch to bring him down and then Gerrard was then cautioned for diving in on McCarthy, despite appearing to win the ball.
A sign of Liverpool's desperation could been seen in the five minutes of injury time when Kyrgiakos went to play up front.
It typified a night when the Reds' short-comings this season were laid bare by an industrious but by no means brilliant Wigan side.