Gomez struck the decisive penalty after Steven Reid had hacked down fellow scorer Victor Moses.
Reid's brilliant free-kick opener had put Albion in front against their relegation rivals.
But Moses netted an equally precise leveller before Gomez had the final say as Albion conceded a penalty for the fourth straight home game.
Baggies boss Roy Hodgson, though, swerved an earbashing at home by not giving one of his own when asked about referee Mike Dean's performance.
He said: "My wife slaughters me for complaining about the penalties and she is probably right, so I prefer to say nothing.
"People can make up their own mind. We will just get on with it. There is no doubt that it was a penalty for their goal.
"If the referee got any of the other decisions wrong, I don't know. Time will tell.
"The TVs will go through the analysis. They will come up with the answers. I will keep my mouth shut."
Hodgson at least took consolation from his side's performance.
He said: "It was one of those days where you find it hard to assess things in the sense that losing at home to team below you in the table should fill you with a lot of regrets and anger.
"But I can't be angry with that performance really because I don't think we can play a lot better than that.
"If we can guarantee playing like that for the next 24 games, then I'll be happy."
Opposite number Roberto Martinez hailed Moses for his superb display just a couple of days shy of his 21st birthday.
The Latics boss said: "I don't think Victor has had a bad spell this season. He has been very consistent.
"He is only 20, he had a great birthday present, on Monday he is 21 and the first goal was as good a finish as you are going to get in this league.
"I know that sometimes playing for Wigan you are not going to get as much credit as playing for other clubs.
"But the way he has been working on a daily basis, he has got huge potential and I've got no doubts that he is going to fulfil it."
Albion started on fire but Chris Brunt was always stretching too far as he tried to convert Peter Odemwingie's cross and the ball went over.
Latics keeper Ali Al Habsi then finger-tipped a powerful 20-yard drive from Brunt on to the bar.
It was non-stop pressure from the hosts and Jonas Olsson glanced a header wide from a Brunt cross and James McCarthy blocked a shot from Jerome Thomas.
Connor Sammon had the first attempt on goal for the Latics but his shot was deflected harmlessly through to Albion keeper Ben Foster.
Brunt was seeing plenty of the ball and his pass found Thomas but his volley from a narrow angle was blocked.
Moses had the first shot on goal for Wigan but dragged his chance a couple of yards wide.
Thomas got in another effort for Albion but the ball deflected over and Gareth McAuley then saw his header come off a Wigan player and flash wide.
A goal was coming and it was Reid who took centre stage as he curled home a superb 25-yard free-kick. But Martinez was unhappy with the deadball award after Gary Caldwell was adjudged to have brought down Odemwingie.
Caldwell made an important block to deny Odemwingie a second for the home side before Wigan levelled through Moses' first goal of the campaign.
Midfielder Youssouf Mulumbu cut out a cross from Mohamed Diame but the ball fell into the path of Moses who curled his shot past Foster.
Albion began the second period on the offensive and Shane Long charged down an attempted clearance from Caldwell before attempting to pick out the run of Brunt with his cross. Maynor Figueroa made a vital headed clearance and Brunt needed treatment before he could continue after the pair collided.
Wigan went ahead on 57 minutes as Gomez's penalty sent Foster the wrong way.
Wigan were growing in confidence and Moses had Foster back-pedalling to collect a long-range chip after spotting him off his line.
Al Habsi produced a low save save to turn aside a header by Long from Nicky Shorey's centre.
Moses had a shot blocked when Sammon was in space on the edge of the Baggies box.
Long almost grabbed Albion a point but his header hit the post from Thomas' centre.