Newcastle dominated the first half as Burnley lost three men - skipper Jason Shackell, Dean Marney and substitute Kevin Long - to a combination of injury and illness, and led 2-1 at the break courtesy of strikes from Steven Taylor and Jack Colback either side of Paul Dummett's own goal.
However, comeback kings Burnley, who fought back from 2-0 down at Manchester City on Sunday to claim a point, responded spectacularly after the break and got their reward when Danny Ings headed them level.
But having also hit the woodwork on four occasions, they looked to be heading for defeat when Moussa Sissoko restored the Magpies' lead 12 minutes from time, only for George Boyd to dash the home side's hopes with four minutes remaining.
Sean Dyche said: "There is a mentality here that is very, very strong, and it's been there all season. People have said to me, 'You must be pleased with the belief now' - I was pleased with it at the beginning of the season.
"The performances over this Christmas period have been absolutely outstanding. How we didn't get anything against Liverpool is a head-scratcher in itself; we were excellent at Manchester City and I thought we were excellent today.
"We have just played five out of the top 10 and taken five points over that Christmas period with a lot of games - very good signs about what we think we can do this season."