Villa went ahead through Darren Bent's penalty but this Premier League game turned Albion's way after midfielder Chris Herd was red-carded after 35 minutes following a clash with Jonas Olsson inside his own box.
Chris Brunt missed the spot-kick but the Baggies cashed in on Villa's frailty at set-pieces with Olsson equalising before half-time and Scharner netting the winner - both from Brunt corners.
It would be fair to say referee Phil Dowd will not be on the Christmas card list of Villa fans after dismissing Herd.
They still remember Dowd's decision not to dismiss Manchester United defender Nemanja Vidic for hauling back Gabriel Agbonlahor during the early stages of the 2010 Carling Cup final.
But victory completed a quickfire derby double for Albion after last week's triumph over Wolves and they have collected 11 points from the last six games.
They overcame the early loss of striker Shane Long through injury and dominated the second half with their numerical advantage and were more inventive with their passing.
Scharner impressed as the midfield enforcer while Somen Tchoyi was a handful for the Villa back four after replacing Long.
Bent squandered a golden chance to put Villa ahead after five minutes.
Barry Bannan failed to make proper contact on his shot but it fell straight to the feet of Bent unmarked eight yards out. The England striker looked certain to score but scooped his shot over the crossbar.
Alan Hutton was booked for a touchline tackle on Long who was replaced after 20 minutes by Tchoyi.
Billy Jones became the first Albion player to be booked for bringing down N'Zogbia.
Villa took the lead after 23 minutes after a mix-up between Steven Reid and goalkeeper Ben Foster.
Reid tried to chest the ball back to Foster but Agbonlahor nipped in and was brought down by the on-loan Birmingham goalkeeper. Up stepped Bent to send Foster the wrong way from the spot.
Herd was impressing in midfield for Villa with his industry and commitment but was sent off after 34 minutes after an apparent off-the-ball clash in the penalty area with Olsson.
Dowd brandished a straight red card before pointing to the penalty spot. Brunt failed to take advantage as he drilled his spot-kick wide.
Villa defender Alan Hutton then suffered a head injury in an aerial clash with N'Zogbia and was replaced by Carlos Cuellar after 42 minutes.
Shay Given produced a fine save to keep Villa in front when he turned aside a shot on the turn from Tchoyi.
But a minute before half-time Olsson brought the Baggies level when he outjumped the Villa defence to head home Brunt's corner.
Albion tried to make their numerical advantage count after the break and Given parried away a fierce drive from Youssouf Mulumbu.
Olsson again climbed above the Villa defence in a replica of Albion's equaliser but this time he headed Brunt's corner over the crossbar.
The visitors were not to be denied and after 57 minutes Scharner put them ahead with Villa again caught out at a corner. Agbonlahor failed to deal with Brunt's corner at the near post and Scharner reacted in an instant and volleyed home via the underside of the bar.
Given was booked after showing dissent when disputing the award of a corner and then Mulumbu was booked for chopping down Agbonlahor.
Villa enjoyed a spell of pressure and James Collins got on the end of a Bannan corner but directed his header wide.
Villa substitute Marc Albrighton then tried to chip Foster but was off the mark.
But Albion still looked threatening on the break and Given came racing out of his box to deny Baggies substitute James Morrison.
Peter Odemwingie should have made it 3-1 in injury time but miskicked with the goal at his mercy.