Newcastle's second win in 13 matches moves them up three places to 13th and they are now four points clear of the relegation zone.
Stoke, who have won only two in 12, drop one place to 16th and remain two points clear of the drop zone.
After defeat, Potters boss Mark Hughes addressed the jeers of home fans: "It's to be expected.
"I think for the last two or three weeks the agenda in the media and social media... that was going to happen.
"It doesn't bother me. What bothers me is the team does better. I have talked about the noise before and it only goes away if you win.
"I remind people that the reason people are disappointed is because of the high standards that have been set here and those high standards were set by me and my staff.
"So we need to do something about it. We will get on with addressing it and turning it around. That's my makeup as a person, a manager and a player."