The Austria international fired home a 72nd-minute winner at the Stadium of Light to leave his former boss at Wigan, Steve Bruce, in the thick of the fight against the drop.
Victory extended the Baggies' unbeaten run to seven games, six of them under new manager Roy Hodgson, and left Sunderland with just a single point from the past 24 they have contested in a disastrous run.
The home side took a 10th-minute lead through Nicky Shorey's own goal - their first strike in seven and a half hours of football - but the impressive Peter Odemwingie, who scored the only goal in the reverse fixture in August, levelled within 19 minutes.
Phil Bardsley's 31st-minute piledriver restored the Black Cats' advantage, but Youssouf Mulumbu finished off a fine 54th-minute move to set the stage for Scharner to snatch victory and a first league double over their hosts in 42 years.
The midfielder's strike sparked mass celebrations among the travelling fans, who had arrived in a fleet of 40 free coaches, but left the remainder of a crowd of 41,586 in a rebellious mood.
Both sides went into the game sitting precariously above the thick of the relegation zone and knowing a win would significantly ease their fears of being dragged into the mire.
But they did so in very different runs of form with Sunderland having taken just a single point from the previous 21, while the Baggies had managed a creditable 10 from 18.
In addition, the Black Cats had not scored in 440 minutes of football, and Bruce's response was to leave out England midfielder Jordan Henderson, Anton Ferdinand, Sulley Muntari and Stephane Sessegnon and restore Nedum Onuoha, Ahmed Elmohamady, Steed Malbranque and Kieran Richardson to the starting line-up.
That allowed him to push Danny Welbeck up front alongside Asamoah Gyan and abandon the 4-5-1 formation which had paid few dividends in the wake of Darren Bent's departure for Aston Villa.
It took Sunderland just 10 minutes to make their mark, although they did so with a helping hand from Shorey.
In his desperation to prevent Elmohamady from reaching Gyan's deflected cross, the full-back only succeeded in heading past goalkeeper Scott Carson off the underside of the crossbar to end the Wearsiders' goal-drought after seven and a half hours.
Bruce's men visibly grew in confidence as they shook off the trauma of last weekend's 5-0 drubbing at Manchester City, although their resurgence was dented within 19 minutes.
Defender Jonas Olsson did well to help on a ball into the box, and it fell perfectly for Odemwingie to fire past goalkeeper Simon Mignolet, his second goal against the Black Cats this season.
However, where the reverse might have prompted a capitulation in recent weeks, it simply served to rejuvenate the home side, and they regained their lead within two minutes.
Richardson tapped a free-kick sideways to Bardsley, who smashed a rising 25-yard drive into the top corner with the help of a deflection off the defensive wall.
Presented with the task of having to work their way back into the game for a second time, the Baggies steeled themselves and went close on the stroke of half-time when Mignolet had to get down well to claim skipper Chris Brunt's curling free-kick.
Bruce, who had had to replace John Mensah with Ferdinand after just 12 minutes, sent on Bolo Zenden for Richardson at the break, and saw skipper Lee Cattermole's goal-bound half-volley blocked as it sped through a crowded penalty area two minutes after the restart.
Good work by Odemwingie allowed Brunt to shoot with 51 minutes gone, but a deflection made Mignolet's job easy.
However, the Belgian was not so fortunate three minutes later when, after Mulumbu had exchanged passes with Odemwingie, his shot clipped Michael Turner and crept inside the far post to make it 2-2.
By now, it was the visitors who were looking the more confident as they dominated possession to leave the home contingent among the crowd with an uneasy feeling.
That sense of unease would have increased markedly had Mignolet not pulled off a fine 69th-minute to keep out Olsson's powerful header after the defender met Brunt's inviting free-kick at point-blank range.
But the Black Cats' afternoon took a further turn for the worse 18 minutes from time when Odemwingie once again created space for himself before crossing for Scharner to blast into the bottom corner.
Sunderland launched a desperate onslaught as time ran down, but Welbeck's injury-time miss, which flew high over the bar, was as close as they came to snatching a precious point.