The home side came from two goals down to draw 2-2 with Rafa Benitez's side.
Dwight Gayle scored both Newcastle's goals, and Jonjo Shelvey should have wrapped up the win.
But the midfielder put a glorious chance wide and Bournemouth struck twice in the last 10 minutes to claim a point.
Ex-Newcastle midfielder Dan Gosling netted the equaliser for Eddie Howe's team.
The result saw Newcastle drop down to 15th in the Premier League table. United are three points above the relegation zone.
United manager Benitez, unusually, named an unchanged starting XI.
Bournemouth – who won 1-0 at St James's Park earlier in the season – set about their visitors, but they couldn't find the target and United started to see more of the ball.
Kenedy shot wide and then put a free-kick of Asmir Begovic's goal before Newcastle got their breakthrough in the 17th minute.
Shelvey played a brilliant ball forward for Matt Ritchie on the right. The former Bournemouth winger delivered a low cross which was eventually backheeled into the net by Gayle.
It got better for Newcastle at the end of the half.
The home side cleared a corner and Paul Dummett delivered a deep cross from the left for Ayoze Perez on the far byline. Begovic failed to stop Perez's delivery and Gayle was left with a tap-in.
After the break United, superbly led by Jamaal Lascelles, were disciplined and organised as Bournemouth probed away looking for a way back into the game.
Newcastle were content to spend much of the second half on the back foot as they looked for chances on the break.
Christian Atsu replaced the erratic Kenedy in the 64th minute after Isaac Hayden came on for Gayle later in the half.
Shelvey had a glorious chance to wrap up the points, but he shot wide from an Atsu cross.
Within seconds, Bournemouth were level thanks to a fine goal from substitute Adam Smith, who beat Martin Dubravka with a shot struck from outside the area.
And Gosling netted an 89th-minute equaliser for the home side from close range.
Bournemouth pressed for a winner in five minutes of added time, but United held on.
NEWCASTLE UNITED: Dubravka; Yedlin, Lascelles, Lejeune, Dummett; Ritchie (Manquillo, 84), Shelvey, Diame, Kenedy (Atsu, 64); Perez; Gayle (Hayden, 78). Subs not used: Darlow, Clark, Merino, Joselu.
BOURNEMOUTH: Begovic, Francis, Steve Cook, Ake, Fraser (Mousset, 63), Lewis Cook, Gosling, Daniels (Smith, 46), King, Wilson (Defoe, 73), Stanislas. Subs not used: Boruc, Surman, Pugh, Simpson.
Goals: Gayle 17, 45, King 80, Gosling 89
Bookings: Ake 52, Ritchie 53, Yedlin 81, Diame 85, Perez 90
Referee: Roger East (Wiltshire)