The Magpies, now in the hands of former Clarets boss Eddie Howe, collected their first success of the season, as well as their first Premier League clean sheet of the campaign.
The breakthrough came five minutes before the break when Nick Pope spilled Joe Willock's delivery following a collision with Fabian Schar.
Callum Wilson was the grateful recipient of the mishap as the striker lifted the ball into the roof of the net, despite the best efforts of Chris Wood on the line.
The hosts, who lost Maxwel Cornet to injury just before Wilson's winner, had earlier hit the post through Johann Berg Gudmundsson.
And substitute Jay Rodriguez had a late finish ruled out as the linesman's flag was raised.
Here are the ratings.
9. Josh Brownhill 5
Wasn't able to contribute anything in terms of creativity, but screened his back four well on the whole, particularly in the first half. The midfielder bust a gut to get back to Saint-Maximin and make an excellent recovery tackle in the first half.
10. Maxwel Cornet 6
Influenced Burnley's play in the first half-an-hour, forcing a fragility in Newcastle's defence. His movement caused issues, his awareness and anticipation likewise, and he went close on two occasions, dragging a shot wide before testing Dubravka with a header. Withdrawn with a thigh strain.
11. Chris Wood 5.5
Tends to take the brunt of the criticism when Burnley fire a blank, but the striker was once again feeding off scraps, at best. Started well, winning flick ons, which led to Cornet's chance, and dropped deep to hold the ball up. Quietened as the game wore on.
12. Matej Vydra 5
Closed both full backs and centre backs in possession, forcing them to clear their lines. His willingness to chase 'lost causes' also won the Clarets throw-ins in advanced positions. However, wasted a golden chance to equalise on the stroke of half-time.