© PA Photos
The Championship's top scorer combined with Manchester United-bound Wilfried Zaha on a number of occasions as the Eagles dominated the opening 45 minutes at Selhurst Park.
A jinking run from Zaha brought about Palace's lead, as he wriggled through two Boro defenders before crossing for Murray, who simply tapped in at the back post.
He could have added to his 26th goal of the season but squandered a pair of Zaha-crafted opportunities, firstly flicking an inswinging cross just wide of the post.
Minutes later, Murray was found unmarked by the England international but sent a seven-yard header over the crossbar.
After being on the back foot for 40 minutes, Middlesbrough threatened to equalise through a succession of chances late in the half.