Gomez put the hosts ahead at the DW Stadium with a brilliant free-kick in the 65th minute and Rodallega deflected in a second five minutes from time.
Struggling Wolves were up against it from the 11th minute, when captain Karl Henry was sent off for a shocking challenge on Gomez, but it was the Wigan midfielder who had the last laugh.
Neither side was able to take control in a scrappy opening, and Wigan found themselves temporarily without captain Antolin Alcaraz in only the seventh minute when he left the pitch to receive stitches in a head wound.
The numbers were then evened up four minutes later, but Henry's exit was to be permanent following a reckless challenge on Gomez.
Referee Lee Mason had no hesitation in brandishing a red card after the Wolves captain launched himself into a challenge on Gomez, catching the Spaniard on the shins.
It was the last thing Henry needed, with the heat already on him and Wolves for a perceived over-physical style of play.
Henry was criticised for a number of challenges on Newcastle's Joey Barton earlier in the season, while he was also the tackler when Fulham striker Bobby Zamora broke his leg.
But neither the 27-year-old nor manager Mick McCarthy, who has been a staunch defender of his players amid the criticism, could have any complaints this time.
Thankfully, and somewhat surprisingly, Gomez was able to continue after treatment, and, with Alcaraz also returning to the action, Wigan set about trying to make their numerical advantage count.
However, if anything the sending-off merely exposed Wigan's lack of invention as they were restricted to a series of wayward shots from distance until just before half-time when Gomez could only deflect Charles N'Zogbia's cross past the far post with Marcus Hahnemann stranded.
Within seconds of the restart, Wigan should have been ahead. At the end of an impressive move, Rodallega found space on the right of the area and passed to Franco Di Santo, who appeared to have the simple task of slotting the ball home from six yards.
But the Argentinian scuffed his shot just enough to allow Hahnemann to get a hand to the ball, and the Wolves defence managed to clear.
Wigan were certainly demonstrating more creativity in attack and, after a good run and cross from N'Zogbia down the left, James McCarthy fired a shot into Hahnemann's midriff.
Wolves boss Mick McCarthy responded by bringing on defender George Elokobi for Fletcher but his plans went out of the window in the 65th minute.
Dave Edwards pulled back N'Zogbia on the edge of the area and Gomez curled a superb free-kick into the top corner to give the hosts the lead.
N'Zogbia, who had been the game's most influential player, created another shooting chance for himself on the right of the area but could not get enough power on his effort to trouble Hahnemann.
Di Santo then nearly caught out the American with a superb dipping volley from 25 yards out, Hahnemann just managing to palm the ball behind for a corner.
Mick McCarthy went for broke with eight minutes to go, bringing on strike duo Sylvan Ebanks-Blake and Marcus Bent for Edwards and Stephen Ward, but it was Wigan who sealed victory with a second goal five minutes from time.
N'Zogbia played a precision through ball for Rodallega, and the Colombian was able to claim the goal after Christophe Berra guided an attempted clearance onto his foot and beyond Hahnemann.
It was the first time Wigan had managed two goals in a league game this season, and it was more than enough to secure a precious three points.
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