Diomansy Kamara's double lifted West Brom's promotion hopes and plunged Leeds deeper into trouble.
New boy Tore Andre Flo headed Leeds in front after only three minutes.
West Brom equalised four minutes later when Jonathan Greening shot home, and Kamara left Hayden Foxe trailing to add a second after 19 minutes.
Kamara curled home a dipping shot for West Brom on the stroke of half-time, and Alan Thompson's 66th minute free-kick was too late for Leeds.
606 DEBATE: Give your thoughts on the match
Leeds manager Dennis Wise:
"I don't understand how they can perform like that in the second half and perform like that in the first half - and I told them so.
"I was disappointed with the goals we conceded. You can't defend as we did, at times we were asleep at the back.
"It's easier to drop off and let them have it. It's braver to be closer to them."
West Brom boss Tony Mowbray:
"The quality of the goals was excellent and we could have scored a lot.
"We carried on our average of three goals a game from the last nine or 10
matches so we're always a threat.
"The longer those statistics go, the more people big them up so it's important to get a victory away from home."
Leeds: Sullivan, Armando Sa, Foxe, Rui Marques, Elliott (Kandol 57), Blake (Moore 57), Nicholls, Thompson (Einarsson 83), Lewis, Healy, Flo.
Subs Not Used: Heath, Howson.
Booked: Blake, Thompson.
Goals: Flo 3, Thompson 66.
West Brom: Hoult, McShane, Curtis Davies, Clement, Robinson, Gera, Greening, Koren, Chaplow, Kamara (Nicholson 89), Phillips.
Subs Not Used: Zuberbuhler, Carter, Rob Davies, Hodgkiss.
Goals: Greening 7, Kamara 19, 45.
Ref: N Swarbrick (Lancashire).