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.
13. Connor Roberts 5
Introduced as a late substitute, replacing Lowton as he made his Premier League debut. Forced to do plenty of running as the game opened up in the final 15 minutes.
14. Jay Rodriguez 5
Introduced for the final 10 minutes as Burnley pushed for an equaliser. Battled well and had a late goal ruled out when straying just offside as he finished a tidy move from the visitors.