The visitors came from behind on three separate occasions to secure a point at St. James' Park.
Sean Dyche's side had fought back from two goals down to take a 2-2 draw from champion Manchester City and once again displayed its fighting spirit on Tyneside.
Newcastle had taken the lead on three occasions in the New Year's Day encounter, only for the visitors to hit back each time.
The pre-match buildup was dominated by the absence of Newcastle manager Alan Pardew, who is set to take the vacant Crystal Palace job.
Stand-in John Carver spoke about wanting to end the "chaos" and he saw his side lead at the break through goals from Steven Taylor and Jack Colback on either side of a bizarre Paul Dummett own goal.
Burnley, which had to make all three changes by halftime due to injuries, hit the woodwork on four occasions, but finally equalized through Danny Ings' header.
Moussa Sissoko thought he had won the match in the 78th minute, only for the visitors to silence the home fans when Boyd's low drive was too fierce for Jak Alnwick to keep out.
The visitors could have been in front with less than two minutes on the clock, but Ashley Barnes's effort crashed against the left-hand post.
Newcastle soon settled, though, and Yoan Gouffran tested Tom Heaton from 20 yards before an unmarked Emmanuel Riviere — playing in place of the suspended Papiss Cisse — headed over.
The hosts' reward came in the 15th minute when local boy Taylor nodded Colback's corner in from 6 yards.
Burnley named an unchanged side for the sixth consecutive match, but was forced into its first change as Jason Shackell limped off to be replaced by Premier League debutant Kevin Long.
The visitors were level in the 19th minute in comical fashion when Dummett failed to deal with a high ball and looped a header over the advancing Alnwick.
Newcastle went from the ridiculous to the sublime to retake the lead seven minutes later as Colback's sweetly struck left-footed shot crashed off the post and into the net for his second goal in as many games.
Burnley's woe deepened as both Dean Marney and Long had to come off before halftime, the latter stretchered from the field with a serious-looking knee injury.
Their bad luck continued after the break when Ings curled an effort against the crossbar and Barnes nodded the rebound against the post.
The woodwork rescued Newcastle for a fourth time when Ben Mee's thumping header shook the bar, though the pressure finally told in the 66th minute when Ings got a cute touch on Michael Kightly's fine delivery to beat Alnwick.
Newcastle pulled ahead again with 12 minutes to go. Ayoze Perez found space in the box to tee up Sissoko, who emphatically finished from close range.
But there was time for one last twist as poor defending from Newcastle allowed Boyd to go clear and the winger — who scored Burnley's goal in a 1-1 draw in last month's reverse fixture — slotted a low effort just out of Alnwick's reach.