Alan Navarro fired an added-time winner as Albion maintained their flying start to 2012.
The midfielder connected with a low drive from the edge of the box to clinch a 2-1 win at Leeds.
It was his first goal for the club.
Craig Mackail-Smith earlier scored his first goal since November to put Albion ahead only for the hosts to reply quickly.
Mackail-Smith was left on the bench but struck just three minutes after coming on for Sam Vokes.
His close range finish on 77 minutes from a superb Vicente corner seemed to have sent Albion on course for a first win at Elland Road in 26 years.
The hosts levelled from a flag kick of their own just two minutes later with Luciano Becchio glancing a header gently inside the unguarded far post.
But Navarro settled it in the first of four added minutes after Vicente threaded through a pass.
Albion, cheered on by 947 travelling fans in a crowd of 23,171, arguably deserved their win in a contest which took a long time to burst into life.
The first half was devoid of goalmouth action, although Gordon Greer did well to challenge Becchio as the home striker looked set to head home Robert Snodgrass's first cross of the game.
Albion took a while to get anything going in attack but, when they did, Navarro saw his volley held by Andy Lonergan, who later pushed away a swerving 25-yarder from Liam Bridcutt.
Lonergan denied both Joe Mattock and Vokes in a hectic start to the second half which also saw Mattock make a crucial challenge in front of his own goal to thwart Becchio.
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