Lee Cattermole broke the deadlock for Sunderland after just five minutes with a blistering strike into the top corner from 20 yards after West Brom defended a free-kick poorly.
The hosts fought back and equalised three minutes before half-time courtesy of Saido Berahino’s penalty after Valentin Roberge was deemed to have fouled Victor Anichebe, although Sunderland were furious with referee Neil Swarbrick’s decision.
Berahino then netted his second of the afternoon on 74 minutes to give West Brom the lead, slotting home Craig Gardner’s wonderful cross from close range.
Alan Irvine was denied a win in his first game in charge, though, as Larsson turned in a Patrick van Aanholt cross to round off a flowing move five minutes from time and earn Sunderland a point.
Irvine, who was paraded on the pitch to good applause prior to kick-off, fielded three of his eight new signings in former Sunderland man Gardner, Andre Wisdom and Sebastien Pocognoli.
Record £10million buy Brown Ideye, not yet deemed match-fit, was left on the bench.
Sunderland gave a start to their headline summer signing Jack Rodwell and also gave a debut to Van Aanholt.
At first it seemed West Brom had settled the better, enjoying some good early possession, but it was Sunderland who showed the first flash of brilliance through Cattermole.
The midfielder collected the ball 25 yards out from Jonas Olsson's headed clearance, steadied himself and unleashed a powerful shot into the top corner which Ben Foster could only get fingertips to.
West Brom were not rocked by the setback and soon settled back into a rhythm which could bode well for the season.
They pieced together some slick moves and utilised the holding-up ability of Anichebe well, although they were initially restricted to long-range efforts.
Captain Chris Brunt went close with a good effort that curled narrowly wide and Pocognoli hit another crisp strike, although Vito Mannone was unconcerned as it drifted wide.
Mannone looked more worried when Berahino found space, but lashed into the side-netting.
Sunderland could have doubled their lead against the run of play when Larsson floated a free-kick into the box, but Roberge headed a clear-cut chance wide.
The visitors were made to pay for the miss, although they could have a legitimate gripe over the penalty after Anichebe appeared to go down at the slightest hint of a shirt-pull from Roberge.
Referee Swarbrick blew instantly, but stoked the tension by taking a few moments to indicate his decision.
When given the go-ahead, Berahino made no mistake with a well-taken spot-kick.
Sunderland lost their composure in the minutes that followed and Berahino benefited from some sloppy defending on a strong run, but Mannone got himself behind his shot.
The visitors survived a scare early in the second half as Mannone flapped and Craig Dawson thought he had forced the ball over the line, but the flag was raised for a foul on the goalkeeper.
Sunderland then started to show some spirit and created chances for Connor Wickham, who volleyed wide, and Steven Fletcher, whose header was ruled out for offside.
It proved a short-lived flurry from Sunderland and the Baggies claimed the lead after 74 minutes.
Mannone saved well from Graham Dorrans' long-range strike, but the ball stayed in play and Gardner was the quickest to react, quickly whipping in high cross to the far post.
Sunderland were still back-tracking and Berahino got ahead of Van Aanholt to tap home his second, to the clear frustration of Mannone, who looked angry with the defence.
Yet the visitors were not done and produced a move almost out of keeping with much of their earlier play five minutes from time.
Jordi Gomez found Van Aanholt down the left and his cut-back was deftly diverted past Foster by Larsson from six yards out.