Sunderland caught the Clarets on an off-day as Jermain Defoe opened his account for the Black Cats in a disappointing day on Wearside.
January signing Defoe and strike partner Connor Wickham both found the net in the first half at the Stadium of Light.
And despite an improved second half from the Clarets, they were unable to find a way back as Gus Poyet’s side picked up their second home win of the campaign.
Sean Dyche named an unchanged starting 11 for the ninth successive Premier League game.
Danny Ings, who will remain at Turf Moor for the rest of this season at least, partnered Ashley Barnes in attack.
There was a tame start to the contest, before The Stadium of Light erupted prematurely in the 10th minute, as Wickham found the net after a foul on Kieran Trippier, which was well spotted by referee Lee Mason.
But it was a solid start from the Clarets and in the 17th minute they were a whisker away from snatching the lead as David Jones swung over a free kick near the right touchline and Ashley Barnes headed just wide.
Trippier then almost caught out Costel Pantilimon with an attempted cross that the keeper caught beneath his crossbar.
Seconds later, in the 20th minute, Burnley trailed though as Anthony Reveillere crossed perfectly from the right for Wickham to nod home from point-blank range.
Burnley fashioned a chance for an immediate equaliser through Ings’ persistence, but as the ball fell invitingly to George Boyd 12 yards from goal, he scuffed his shot on the turn and a grateful Pantilimon saved comfortably.
Eleven minutes from half time though, the hosts doubled their advantage with a fine goal.
Van Aanholt timed his run perfectly in behind Trippier to race onto Jordi Gomez’s pinpoint ball and cross for Defoe to convert the simplest of chances.
That left the Clarets a mountain to climb – and Defoe perhaps should have added to his tally straight from the restart as he duffed a shot straight at Tom Heaton following a sweet passing move.
Burnley knew they had to grab the next goal to try and spread nervousness among the home ranks - and 10 minutes in came the chance.
Boyd created room for a cross that fell to Barnes, but his header from a static position bounced kindly for Pantilimon.
Now though Burnley enjoyed their best spell and when Ings cut the ball back for Barnes, the striker’s low shot from the edge of the box took a deflection just wide of the post.
And after Scott Arfield fired over from a tight angle, the Clarets made a double substitution, Ings and Boyd making way for Lukas Jutkiewicz and former Black Cat Ross Wallace.
Sam Vokes joined them for the final 15 minutes, replacing the tireless Barnes as Sean Dyche looked for a lifeline.
But when Ben Mee’s looping header from a Wallace corer dropped just the wrong side of the post, you sensed this would not be the day for another of those late fightbacks.
BURNLEY: Heaton, Trippier, Shackell, Keane, Mee, Arfield, Marney, Jones, Boyd (Wallace 61), Barnes (Vokes 76), Ings (Jutkiewicz 61).
Subs: Gilks, Kightly, Reid, Duff
Booked: Marney 90
SUNDERLAND: Pantilimon, van Aanholt, Bridcutt, Larsson, Wickham (Graham 75), Johnson (Alvarez 85), Gomez, Reveillere, O’Shea, Vergini, Defoe (Fletcher 75).
Subs: Jones, Coates, Giaccherini, Mannone
Booked: Johnson 68, Larsson 88, Pantilimon 90
Ref: L Mason