Barton rifled in a ninth minute penalty and Obafemi Martins celebrated his 24th birthday with a second just before the break, as Joe Kinnear's side moved out of the bottom three.
It was Kinnear's first win in his first four games in charge as Newcastle moved up to 15th spot, while the Baggies have now been on the wrong end of three successive defeats.
Newcastle completely dominated the first half and could easily have gone ahead after just 30 seconds when Damien Duff played in Ameobi whose shot was hacked clear.
Then after two minutes a long Shay Given clearance was headed on by Shola Ameobi and a Martins drive flicked off Ryan Donk and was clawed over the bar by Scott Carson.
At half time this was a game that looked all but over, but typical of Newcastle they lost their way when substitute Ishmael Miller struck midway through the second period to inflict a nervous finish for the Geordies.
An opening goal for United seemed only a matter of time and it duly arrived after nine minutes after Ryan Donk sent Ameobi crashing inside the box.
Barton quickly seized the ball to make it known he was putting himself on the spot and proceeded to sent Carson the wrong way.
With five spread across the centre of the park it was the start that West Brom did not want and it could have been much worse on the quarter hour.
A Duff run ended with a block and the ball fell invitingly Barton running at pace, but he could not keep his 20-yarder on target.
Then after 37 minutes the Baggies carved open their best chance with a flowing move that let in James Morrison, but the former Middlesbrough player saw his shot deflected over the bar off the right knee of Given.
At the other end good work from Ameobi ended with Habib Beye blazing over, but it was only a temporary respite for West Brom as Newcastle doubled their lead three minutes before the interval.
Beye made another good break down the right and crossed for Martins to get in a header that deflected off Gianni Zuiverloon on its way into the net.
In a bid to add some extra firepower the Baggies took off Chris Brunt after 54 minutes and sent on Miller.
And the Baggies had an immediate chance to reduce the arrears, but Morrison scuffed his effort in what was a good start to the second half by Tony Mowbray's side.
Miller's arrival and his powerful presence posed plenty of problems and he did pull back a goal after 65 minutes, when he latched on to a slide-rule pass from Robert Koren to round Given and fire into the empty net.
After dominating the centre of the park in the first half Newcastle lost their superiority after the break.
And after being floored by a free-kick at Sunderland on Saturday, Newcastle almost suffered the same fate after 73 minutes when Morrison's edge of the box kick was blocked and Miller reacted to the rebound first, only to be bravely denied by Given.