The centre half's pair of close-range finishes gave Eddie Howe's side a 2-0 lead at half time at Villa Park, after their confident start caught the hosts on the back foot.
Alex Moreno then inadvertently applied the final touch to Jacob Murphy's attempt shortly after the break to put the Magpies in control, and though Ollie Watkins' strike preceded a spell of pressure from the hosts, they couldn't haul themselves back into the contest as the points headed back to Tyneside.
As an energetic opening gave way to end-to-end action, United looked to seize the upper hand. Anthony Gordon, lively as ever, pounced on a Murphy through ball and turned Ezri Konsa, but couldn't find a way past Emi Martinez in the hosts' goal. Alexander Isak - who had to be replaced through injury later in the half - curled wide as the visitors kept the pressure on.
Aside from Matty Cash's hopeful effort which Martin Dúbravka saved with ease, Villa offered little in the final third, and Newcastle looked the likelier to go ahead. When Martinez spilled a low Murphy drive, Sean Longstaff looked set to break the deadlock, and surely would have done had it not been for a terrific sliding challenge from Clement Lenglet.
Bruno Guimarães found Gordon with a ball over the top on the half hour and, after the former Everton man's shot was deflected over, Howe's side took the lead from the resulting corner. Kieran Trippier's delivery dropped invitingly in front of goal and Schär did well to wriggle free of Konsa and direct the ball into the bottom corner.
Three minutes later, the Switzerland defender did it again to make it 2-0. Another Trippier corner was cleared out to Gordon, whose 20-yard volley skipped up after a deflection and thumped the crossbar, with Martinez beaten. Schär was quickest to react, slamming home from close range to put the Magpies in complete command.
The only downside of the first half for those in black and white was Isak's injury, but seven minutes after the restart the Swedish frontman's side went further ahead in his absence. His replacement, Miguel Almirón, raced onto a Gordon lay-off and provided a superb cross across the face of goal which Murphy met, with Moreno turning the ball in before crashing into the upright.
Had it been credited to him, Murphy would have deserved the goal for a strong showing down the right wing, but the game began to turn a little after the introduction of another winger. Leon Bailey was brought on by the hosts and, after some brief half-chances for Moussa Diaby and Watkins, began to make his presence felt. Dúbravka did well to keep out another Cash drive from a tight angle but with just under 20 minutes left, Bailey's centre was met by Watkins, who reduced the deficit with an emphatic finish.
Moments later, the England forward thought he'd grabbed a second when he dinked over Dúbravka, but after a VAR check the goal was ruled out for offside. The decision seemed to stem the flow of Villa's late rally, and the closing stages were relatively comfortable for United, who could even have made it four at the death when Longstaff was denied by Martinez.
