Albion have a crucial lead at the Amex and are halfway to three points which would all but secure their Premier League status.
Danny Welbeck was yanked down by Egzan Alioski and referee Chris Kavanagh had no hesitation in giving a spot kick.
Pascal Gross dispatched the penalty into the bottom just past the dive of Leeds keeper Illan Meslier to put Albion in front.
Jack Harrison had a chance for Leeds but this was tidied up by Dan Burn after the ball ricocheted across the area.
Albion had other opportunities to score, with Danny Welbeck playing in Leandro Trossard who fired high and wide with Meslier beaten.
Then Welbeck, when well placed after sprinting into the penalty area, shot wide.
Dan Burn did well to block a Tyler Roberts effort after good work from Stuart Dallas.
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