Poyet's men secure safety with fourth straight win.
Goals from Jack Colback and Fabio Borini sunk West Brom as Sunderland secured their Barclays Premier League status with a convincing victory.
The Black Cats chalked up four straight top-flight wins for the first time since December 2000 as they blew the Baggies away with two stylish strikes in a high-octane first half.
Colback capped a purposeful start with a 13th-minute opener, added to by Borini's brave finish just before the half-hour.
And that was enough for Sunderland, who came close to a third goal through Santiago Vergini and sub Jozy Altidore in the second half.
The result saw Poyet's side made it an incredible 13 points from their last five games to move up to 14th in the league.
With his team in such a rich vein of form, it was no surprise that Sunderland's head coach named the same starting eleven for the fifth successive game.
The Uruguayan knew a point would almost certainly be enough to secure safety due to Sunderland's goal difference but had spoken of his attacking intent in the build-up to the game.
His side duly set the tone by starting brightly, with Borini seeing a 25-yard piledriver spectacularly tipped over by Ben Foster eight minutes in.
And the resulting corner from Larsson flashed dangerously across the goalmouth without anyone being able to get the final touch.
That was a portent of what was to come, and it wasn't long before the hosts broke through as Colback selected a great time to slot home his third goal of the campaign.
Marcos Alonso put in a superb cross after scampering down the left, and Colback ghosted between two defenders to loop a shot over Foster's outstretched hand and into the net.
The breakthrough nearly took the roof off a delirious Stadium of Light as the home fans celebrated a vital moment.
Far from sitting back, Poyet's men kept their pedal to the metal as they pressed home their advantage.
Lee Cattermole's magnificent angled ball released Adam Johnson down the right, and the winger raced into the box but was unlucky to see his cross poked away with onrushing team-mates arriving in numbers.
Sunderland's confidence was clearly flowing as they won ball after ball, pouring forward with regularity and dominating possession against an Albion side offering little.
And the hosts doubled their money with a strike of real quality just after the half-hour.
Borini laid a neat ball off to Larsson before continuing his run beyond a static West Brom back line, and the Swede clipped a delightful ball through for his colleague to slam a brave volley past the advancing Foster for his third goal in four games.
The Italian collided with the West Brom keeper as the ball flashed into the net but was quickly on his feet and in the midst of his trademark celebration.
The lead reflected Sunderland's dominance, though Vito Mannone was forced into a good save in the final moments of the first period when he pushed away a right-footed curler from Saido Berahino.
West Brom boss Pepe Mel was clearly unhappy with his side's first-half performance, making two changes at the break, and the alterations sparked the visitors into life.
One of those subs, Craig Dawson, provided a cross which was missed by the sliding Victor Anichebe by a matter of inches before Berahino cut in off the left wing to drill the ball past the near post.
Sensing a need to make a change, Poyet introduced Altidore and Liam Bridcutt on the hour, with Johnson and Connor Wickham making way.
The Uruguayan's substitutions served to neutralise West Brom's momentum, and it was almost 3-0 when Colback's lovely cross picked out Altidore, who struck his first-time shot wide of the back post.
Then a flowing cross-field move saw marauding right-back Vergini released in space, but the Argentinian's angles were just off as his low drive fizzed past the foot of the post with Foster beaten.
The atmosphere intensified as time ticked away, with Sunderland edging ever closer to survival.
A lovely Altidore through ball released Cattermole with seven minutes to play, but the midfielder's shot was blocked before he was substituted late on to a raucous standing ovation following a memorable and typically committed performance.
Mannone saved well from James Morrison late on to secure a third successive clean sheet before the final whistle was greeted by a huge roar as Barclays Premier League safety was confirmed.
Poyet embraced his players at the end before celebrating with the fans, marking mission accomplished ahead of the season finale against Swansea following a remarkable turnaround.
- Cattermole (Giaccherini)
- Wickham (Altidore)
- Johnson (Bridcutt)
- Reid (Dawson)
- Berahino (Vydra)
- Yacob (Mulumbu)