The Austria international snatched victory five minutes from time as a five-goal thriller went the way of the visitors.
Roy Hodgson's men took the lead on three occasions as Peter Odemwingie and Gareth McAuley with his first goal for the club struck before the break.
However, on both occasions, Demba Ba dragged Newcastle back into it, firstly with a fiercely-struck free-kick and then with a close-range 81st-minute finish.
However, the Baggies refused to accept a point and Scharner made the most of a poor defensive display to claim a victory that leaves the Magpies with just two points from the past 18 they have contested.
Games between the two sides over the past two seasons have been close with three of their past four league encounters in the Championship and Premier League ending all square.
The last of them came on the final day of last season when the Baggies fought their way back from a 3-0 half-time deficit to claim a point which cost the Magpies a top-10 finish.
But if Alan Pardew's side were forewarned, they failed to take heed and found themselves training at the break after an eventful first 45 minutes.
They fell behind with 20 minutes gone when attack turned to desperate defence within seconds.
Cheick Tiote's pass was cut out by Nicky Shorey, who fed the hugely impressive Chris Brunt and watched as he produced a superb defence-splitting pass to put Odemwingie in behind Fabricio Coloccini.
The striker controlled deftly before firing confidently past keeper Tim Krul off the foot of the post to silence the home fans among a crowd of 51,060.
Ba thought he had levelled within two minutes when he drilled home from Leon Best's knock-down, but an offside flag ruined his celebrations.
But in the event, West Brom's lead lasted just 14 minutes and was cancelled out in equally spectacular style.
Gabriel Obertan embarked on a rare foray in-field from the right wing and went down under Jerome Thomas' clumsy challenge 20 yards out.
Ba stepped up to take charge of the resulting free-kick and there was an inevitability about what would follow as he curled the ball high to Ben Foster's left with the keeper unable to deny the Senegal international despite getting a hand to the ball.
Newcastle, who had wobbled alarmingly in the wake of Odemwingie's strike, attempted to capitalise on their equaliser, but they were caught again with a minute of the half remaining.
Brunt, who proved a threat throughout, floated a free-kick to the far post, where Scharner was allowed to helped it back across goal for McAuley to score from close range.
Midfielder Haris Vuckic, starting his first Premier League game, thumped an injury-time drive against the bar with Foster beaten, and the visitors survived to go in ahead at the break.
Ryan Taylor replaced young Italian left-back Davide Santon before the restart, and his side resumed with a flurry.
Obertan saw an early effort deflected wide by McAuley, and Ba curled a 49th-minute shot past the far post after cutting inside from the left.
However, the game might have been over four minutes later when Youssouf Mulumbu once again carved Newcastle open to put Shane Long in on goal.
The Republic of Ireland international seemed certain to score as he rounded Krul with ease, but his shot from a tight angle came back off the crossbar to let the home side off the hook.
Foster got down well to claim Best's curling 54th-minute effort, and the striker's evening ended seven minutes later when he was replaced by Frenchman Hatem Ben Arfa.
Shola Ameobi soon followed as Obertan, who had volleyed over seconds earlier, made way, but Brunt caused concern for Krul when he curled just wide from distance with 73 minutes played.
But after Krul had saved from Long, it was Ba who dragged the Magpies back into the game, converting Ben Arfa's 81st-minute pass with relish.
Vuckic might have won it with a dipping long-range effort which Foster had to turn over, but the Magpies were caught once again at the death when Scharner stabbed the ball past the helpless Krul from Odemwingie's header.