The Spaniard struck after 21 minutes and then again 10 minutes into the second half after first Jose Fonte and then James Ward-Prowse, who was sent off for his pains, fell foul of referee Mike Jones with striker Danny Graham the man causing the problems on both occasions.
In the meantime, Sadio Mane had drawn the visitors level when he capitalised on keeper Costel Pantilimon's error, but the Saints were far from at their best as they slipped to a 2-1 defeat in front of a crowd of 39,613 at the Stadium of Light.
It was just the Black Cats' sixth win of the league campaign and only their fourth at home, and it could hardly have been any more welcome with Dick Advocaat's men, for whom Adam Johnson made a late appearance as a substitute, having slipped into the bottom three last weekend.
They ran out knowing neighbours Newcastle had done them no favours at all by capitulating horribly at resurgent Leicester in the day's early kick-off, and that victory was a must given their challenging run-in.
Southampton, as befits a team challenging for European qualification, started the brighter, but it was the Black Cats who took the lead with 21 minutes gone.
Graham, who turned in arguably his best performance to date for the club, ran on to a bouncing ball inside the penalty area and was caught in the face by Fonte's flailing high boot, leaving Mr Jones little option but to point to the spot.
Gomez stepped up to slot the resulting penalty firmly into the corner with former Sunderland keeper Kelvin Davis powerless to resist, and the home side had the start they craved.
But the locals had barely settled back into their seats when the lead evaporated in chaotic style.
There seemed to be little danger as Nathaniel Clyne's long ball sailed towards 6'7" Pantilimon, but defender Sebastian Coates inexplicably ran into his own keeper and as the pair collided with team-mates John O'Shea, the ball squirmed from his grasp.
Scarcely able to believe his luck, Mane calmly steered his shot into the vacant net to restore parity and leave Advocaat's side back at square one.
To their credit, Sunderland responded to the reverse and it was they who looked the more likely to score as the half wore on despite losing O'Shea with concussion.
Indeed, they might have done so on three occasions with Jermain Defoe curling a 26th-minute effort wide with Sebastian Larsson perhaps better placed outside him and Connor Wickham side-footing over the bar six minutes before the break.
But it was Graham, still awaiting his first goal for the club on his 27th appearance, who thought his time had come on the stroke of half-time when Wickham and Defoe combined inside the box and the ball fell to him at the far post, but he could not get his shot away as the blue shirts arrived en masse.
Coates' afternoon almost took a further turn for the worse six minutes after the restart when he passed the ball straight to half-time substitute Filip Djuricic, but he fired just wide.
But the game's third goal arrived four minutes later and it did so at the other end with Graham once again the protagonist.
He ran on to a long ball and out-muscled defender Maya Yoshida before squaring for the fast-arriving Defoe, who was bundled to the ground by Ward-Prowse.
Once again, Mr Jones had little hesitation in awarding the penalty and dispatched the midfielder to the dressing room with a red card.
Gomez was nerveless as he defeated Davis from 12 yards for the second time to put the home side back in front.
Southampton dominated possession as they looked for a way back into the game with Sunderland looking nervous on the ball, but a strangely toothless display failed to yield any reward with Pantilimon pulling off a fine injury-time save to deny substitute Steven Davis.
Source : PA
Source: PA