Callum Wilson’s seventh goal of the season from the penalty spot gave Newcastle a 1-0 lead going in at half-time.
Wilson then doubled The Magpies’ lead in the second half with a simple tap-in from Allan Saint-Maximin’s smart pass.
Maxwell Cornet then pulled a goal back for Burnley as they fought to remain in the Premier League but it wasn’t enough as the game ended 2-1.
The result confirmed Burnley’s relegation to the Championship as Leeds United survived the drop.
Eddie Howe made two changes to the side that beat Arsenal 2-0 at St James’s Park on Monday night with Kieran Trippier and Jamaal Lascelles coming in for Emil Krafth and Fabian Schar.
It was Trippier’s first start for Newcastle in over three months as he faced his former club following after recovering from a broken metatarsal.
1. Martin Dubravka - 7
Was comfortable when called upon but could have done little about the equaliser after parrying the initial shot.
Photo: Stu Forster
2. Kieran Trippier - 7
Still shaking off a bit of rustiness on his first start in over three months but grew into the game well with some important challenges.
Photo: PAUL ELLIS
3. Jamaal Lascelles - 7
Was reasonably solid at the back with some important clearances and interceptions.
Photo: Ian MacNicol
4. Dan Burn - 7
Got away with a couple of questionable decisions early on but made some crucial challenges as Burnley pushed.
Photo: Stuart MacFarlane