The victory ends a run of five straight defeats in all competitions for Newcastle and will ease the pressure on Howe, at the same time catapulting the side back into the equation for European football next season.
Goals from William Osula, Dan Burn against his former side and Harvey Barnes sealed three points against an in-form Brighton team that had won six and drawn one of their previous eight Premier League fixtures.
Newcastle rode their luck at times with uncertain goalkeeping from Nick Pope and several misses from Brighton, not least Yankuba Minteh, who blazed over from a few metres out at the back post with the score at 2-1.
"It felt very good, in the changing room before the game we knew today was important for us, chasing European football for next season. The points are crucial, we keep dreaming and believing," Newcastle captain Bruno Guimaraes said.
"It was a tough game, Brighton are a good team. Today for everything we have done, we deserve the win. They had a lot of chances. In the first half we were better but second half they were better. I am glad we could keep three points."
Newcastle climb to 13th place with 45 points from 35 games, now five points behind seventh-placed Brighton.
"We are looking up not down. We can still play European football next season, we must win the next three games," Guimaraes said.
Newcastle travel to Nottingham Forest and Fulham, and have a home game against West Ham United remaining this season.