On 17 minutes the Chelsea loanee almost grabbed himself a debut goal, curling an effort from 20-yards out towards Nick Pope, who tipped the ball onto the post.
On 33 minutes Newcastle won a penalty through Kenedy, who was taken down by Phil Bardsley, but Joselu's tame side-footed effort failed to trouble Pope.
Rafael Benitez's charges did not let their heads drop and continued to push forward, although they could not find the breakthrough come the half-time whistle.
The hosts finally succeeded in breaking the deadlock on 66 minutes, when Kenedy's fine display was rewarded with an assist, crossing at the near post for Jamaal Lascelles to head home.
However, Sean Dyche's charges drew level just five minutes from time through a Darlow own goal, when the goalkeeper parried Sam Vokes's header onto the bar but the ball then bounced off the back of his head and into the net.
Burnley's equaliser proved to be the last significant action of the game as the final whistle blew on a share of a spoils for both competitors on Tyneside.
NEWCASTLE UNITED (4-2-3-1): Darlow; Yedlin, Lascelles, Clark, Dummett; Merino, Diame; Atsu (Murphy 64'), Perez, Kenedy (Ritchie 72'); Joselu
BURNLEY (4-2-3-1): Pope; Bardsley, Mee, Long, Taylor; Cork, Westwood (Vokes 70'); Gudmundsson (N'Koudou 83'), Hendrick, Arfield (Lennon 59'); Barnes