The Magpies looked on course for a valuable three-point haul through Jamaal Lascelles’ header, which came from a corner delivered by debutant Kenedy.
United were good value for their lead at that point, and Joselu – who had already missed from the spot in the first half – ought to have doubled it after being played in by substitute Jacob Murphy, only to drag the ball wide of the target.
And, the sting in the tail arrived five minutes from time, as substitute Vokes forced the ball over the line as the Magpies failed to deal with an in-swinging corner.
Just as they did against Chelsea at Stamford Bridge on Sunday, Newcastle made the more purposeful start. After a corner from the left was only half-cleared, Ciaran Clark got up well to meet a dipping Kenedy cross, but just failed to keep his header on target. The Brazilian then came within a whisker of finding the net himself, stepping inside before hammering a left-footed effort against the far post.
The Clarets started to get a foothold, and – had Kevin Long been a little more expectant – they might have taken the lead. Jóhann Berg Guðmundsson delivered a deep free kick from just inside United’s half, but the defender – unmarked – failed to get the ball under control, and a decent chance went begging.
The best opportunity of the first half, however, came and went after 34 minutes. After Kenedy was brought to the ground by Phil Bardsley, Joselu stepped up from 12 yards, but his right-footed attempt was too close to Nick Pope, who pushed the ball away.
Clark came close again for Newcastle before the interval, bringing an acrobatic stop out of the Burnley ‘keeper after meeting another Kenedy delivery at the back post.
There was a chance at either end early into the second half. The first of those fell the way of Joselu, who rose high to meet Kenedy’s corner six yards out before planting a header over the crossbar. Just a minute later, Ashley Barnes found himself in on goal after gathering Jeff Hendrick’s flick-on, but the forward curled off-target with just Karl Darlow to beat.
On 65 minutes, a neat passage of play saw Kenedy presented with a chance to shoot, but the wide-man’s effort deflected wide.
However, from the resultant corner, Newcastle finally broke the deadlock. The Brazilian swung it in, and Lascelles leapt off the ground to guide the ball beyond Pope and into the far corner.
Joselu squandered a golden chance to seal the deal for United with just less than 20 minutes to play. Murphy led a swift Magpies break before threading the ball through to the Spaniard, who was only able to fire wide of the far post with just Pope to beat.
With just five minutes left, it was to cost Rafa Benítez’s side dear. Moments after Aaron Lennon forced Darlow into a close-range stop, Newcastle failed to clear a corner from the left, and Long’s glancing touch dropped into the path of Vokes, whose header just had enough on it to beat United’s stopper.
The Magpies looked flattened after that, and were unable to launch one final siege on the Burnley goal. They do, however, climb a single place in the Premier League ahead of Sunday’s trip to Crystal Palace.