The win moved 17th-placed Newcastle four points clear of the relegation zone, with 21 points from 23 games. Villa are six points ahead in 11th.
Newcastle had a penalty overturned by VAR in the 33rd minute when a Calum Chambers foul on Joe Willock was deemed to have taken placed outside the box, but Trippier blasted the resultant freekick through the Villa wall to give the hosts a deserved lead.
Villa showed more adventure after the interval and Ollie Watkins had the ball in the net with a reaction header just after the hour-mark, only for the goal to be disallowed for offside following another VAR check.
Clear goal-scoring opportunities, however, were in limited supply for both sides as Newcastle completed the job with a tidy defensive display for their second straight league victory.
"Three more points feels good from where we have come. But even in this good moment we are very calm but very pleased," Newcastle manager Eddie Howe sad.
"We didn't give up too many chances to Aston Villa. It was a tight game and in weeks gone by we wouldn't have won this game. There is still a heck of a long way to go."
Villa manager Steven Gerrard bemoaned his side's poor performance.
"We were honest with the players at halftime and we got a bit of a reaction but I've got no complaints with the result. I believe you make your own luck away from home and we were nowhere near it today," Gerrard said.
"I expect more from this team collectively and individually. We feel frustrated and disappointed."