The Switzerland centre-back rifled home an unstoppable shot midway through the first half before Sean Longstaff scored his first league goal for the club.
Burnley had battled to a 2-1 win over Tottenham just three days ago, but they rarely troubled Newcastle goalkeeper Martin Dubravka in the second half as a run of four away league games without defeat ended rather meekly.
It took 24 minutes for a shot on target to arrive, but it was worth the wait for Newcastle fans, with Schar blasting a stunning effort in off the right-hand post from 25 yards out.
Dubravka blocked a Chris Wood effort as Burnley threatened a swift response, but it was 2-0 seven minutes before half-time, Longstaff drilling a shot into the bottom-left corner after the visitors failed to clear Matt Ritchie's cross.
There was more frustration for Burnley before the break, with Ritchie escaping punishment for a late challenge on Johann Gudmundsson in the box, and James Tarkowski volleying over when presented with a golden chance to score.
Tarkowski headed over from Robbie Brady's corner, but Miguel Almiron should have made the win safe when he raced through on Tom Heaton's goal only to fail to beat the keeper at his near post.
Peter Crouch was thrown on but could do little more than leave Mohamed Diame needing treatment for a cut head after an accidental collision, as Burnley lost for just the second time this year in all competitions.
1 - Fabian Schar's goal was Newcastle's first to be scored from outside the box in this season's Premier League, with Ayoze Perez the last to score from outside the box for the Magpies in the competition (in April 2018 against Leicester City). Strike.— OptaJoe (@OptaJoe) February 26, 2019
What does it mean? Newcastle put daylight between themselves and bottom three
Newcastle are now up to 13th in the table, a point and two places above Burnley, after a third home win in a row in the top flight.
21y 119d - Aged 21 years and 119 days, Sean Longstaff is the youngest player to score for Newcastle in the Premier League since Rolando Aarons in May 2016 (20y 181d v Spurs). Talent. pic.twitter.com/3dinaQSG9e— OptaJoe (@OptaJoe) February 26, 2019
Longstaff keeps it cultured
Composed on the ball and accurate in his passing once more, Longstaff got on the scoresheet with a fine finish. His stock continues to rise in these parts.
Tough trip for Tarkowski
Less-than-resolute in his own half or when in possession, Tarkowski also wasted two of Burnley's best chances to score. It was not one of his finest outings.
Key Opta Facts
- No side has picked up more Premier League points at home in 2019 so far than Newcastle’s 12 (P5 W4 D0 L1), with only Arsenal and Manchester City matching their tally on home soil.
- Newcastle have won four consecutive home league games for the first time since last April; they had won just two of their opening 11 home league games of this season prior to this streak (D1 L8).
- This was the first time Burnley have lost a Premier League game with Tom Heaton in goal since August 2017 against West Brom (0-1), ending a 10-game unbeaten streak for the goalkeeper in the competition.
- Newcastle have done a league double over Burnley for the first time since the 1954-55 top-flight campaign; they had won just two of their previous 11 league games against the Clarets before this season (D4 L5).
- Schar's goal was Newcastle's first to be scored from outside the box in this season's Premier league from their 121st such attempt from outside the area in 2018-19, with Perez the last player to score from outside the penalty area for the Magpies in the competition in April 2018 against Leicester City.
- Aged 21 years and 119 days, Longstaff is the youngest player to score for Newcastle in the Premier League since Rolando Aarons netted aged 20 years and 181 days against Spurs in May 2016.
Newcastle head to West Ham on Saturday, while Burnley will host Crystal Palace.