Villa suffered their first home league defeat of the season, with Switzerland defender Schar scoring both goals from close range.
Alex Moreno’s own goal gave Newcastle a three-goal lead until Ollie Watkins scored.
Watkins had the ball in the net for the second time, but was called offside.
Villa missed out on the opportunity to close the gap on Premier League leaders Liverpool, and they now sit fourth, five points behind the Reds despite having played one more game.
Newcastle moved up to seventh position in the rankings, but they are still nine points behind Villa in the race to qualify for the Champions League next season.
Premier League match reactions and analysis on Tuesday.
Schar’s energy reinvigorates Howe’s side.
The Magpies played with more panache against a Villa side who had collected 28 points out of a possible 30 at home prior to this match, and they were well-deserved winners.
Anthony Gordon, in particular, led their attacking play with cunning and flair, regularly outfoxing the Villa defence with his mobility and trickery.
Similarly, Alexander Isak appeared a threat in attack until being forced to leave early in the first half due to injury.
But Eddie Howe will have been particularly pleased with the substance of his team, as well as the eye-catching moments of elegance, as they secured only their second away win of the season.
Schar was the epitome of that: disciplined, gritty, and organized in his defensive effort, he never shied away from a block or challenge. On the opposite end of the pitch, he was clinical.
Schar provided Ezri Konsa the opportunity to score after Villa’s defenders failed to prevent Kieran Trippier’s corner from dropping into the six-yard box.
Newcastle’s second goal was pure opportunism from Schar. He remained in the area after a corner and punched the ball home after Gordon’s deflected shot bounced off the underside of the crossbar, with Emiliano Martinez already committed.
Seven minutes after halftime, Moreno couldn’t help but slide Jacob Murphy’s low finish into the net.
Newcastle regained energy and intensity following a downturn. If the FA Cup fourth-round win over Fulham last weekend signaled the beginning of recovery, there is now even more reason to be optimistic.
