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.
5. Matt Targett - 7
Played several good balls forward for Allan Saint-Maximin to chase down and made a crucial header off the line to deny Tarkowski. Another solid performance, hopefully not his last in black and white. Photo: Naomi Baker
6. Bruno Guimaraes - 7
Rarely troubled in possession and got stuck in to frustrate the home side and their supporters. Slipped at a crucial moment as Newcastle looked to make it 3-1. Photo: Ian MacNicol
7. Sean Longstaff - 8
Another very good performance in the middle of the park as he closes in on signing a new deal. Tackled well and was tidy in possession. Photo: David Price
8. Joelinton - n/a
Had a couple of decent touches before being forced off early due to injury. Photo: Ian MacNicol