Robert Earnshaw scored both goals as Bryan Robson won his first game in charge of West Brom.
Earnshaw had already seen one effort cleared off the line by Robert Kozluk when he converted a Jason Koumas cross.
And Earnshaw made sure of victory when he lobbed the ball over Andy Lonergan close to full-time.
Lonergan had earlier made good saves to deny Zoltan Gera and Rob Hulse while Kozluk, Chris Lucketti and Chris Sedgwick went close for Preston.
Preston started well without creating any real openings before West Brom asserted themselves on the tie, winning three corners in succession.
Gera came closing to putting the visitors in front but Lonergan got down sharply to save the Hungarian's snap-shot.
Sedgwick saw his looping volley narrowly miss Russell Hoult's goal, while skipper Lucketti headed narrowly wide from Youl Mawene's floated free-kick as Preston pushed forward.
But WBA continued to create openings of their own - Hulse rising above Graham Alexander but heading wide, and Earnshaw miscontrolling at the crucial moment when well placed at the far post.
And the visitors continued to display a superior cutting edge after the break, with a quickly taken free-kick catching the North End defence static.
Hulse got the better of Lucketti and diverted the ball goalwards but Lonergan made a great save with his feet.
Earnshaw then had the ball in the Preston net with a neat dink over Lonergan but the goal was ruled out for offside.
Midway through the second-half Preston enjoyed a spell of pressure, with Alexander shooting wide from long distance and Rob Kozluk narrowly missing the target with a curling shot after cutting inside from the left.
West Brom bounced back and Earnshaw shot past Lonergan but Kozluk cleared the ball off the line with Gera lurking.
Earnshaw's frustration was short-lived as he neatly diverted Koumas' cross past Lonergan for the opener.
And his cheeky second - lifting the ball over the advancing Lonergan from an acute angle - sealed victory for Bryan Robson's beleaguered side.
Preston boss Billy Davies:
"If the game finished 0-0 nobody would have complained.
"I don't think we were at it like we have been in the last few weeks and I said that to the players after the game there.
"Goals are important. But we didn't defend them, and they were two very disappointing goals to lose."
West Brom boss Bryan Robson:
"It's nice to get a win under our belts. We had a good fan base here and we've sent them home happy.
"It's pleasing, because I thought it was a good solid performance by us today. These ties can be awkward.
"It's nice to get the first win but it'll be nicer to get the first win in the Premiership - we know how important that is. Even so it's good for the lads' confidence to win here."
Preston: Lonergan, Alexander, Kozluk, Lucketti, Mawene,Sedgwick (Mears 84), Etuhu, McKenna, Lewis,O'Neill (Jackson 67), Agyemang.
Subs Not Used: Ward, McCormack, Davis.
West Brom: Hoult, Albrechtsen, Clement, Purse, Robinson, Gera,Johnson, Wallwork, Greening (Koumas 73), Earnshaw,Horsfield (Hulse 19).
Subs Not Used: Scimeca, Gaardsoe, Kuszczak.
Booked: Hulse, Albrechtsen, Koumas.
Goals: Earnshaw 76, 83.
Ref: G Laws (Tyne & Wear).