Dwight Yorke put the Black Cats ahead, side-footing past Dean Kiely after a neat flick-on from Stern John.
John doubled the lead four minutes after the break, left unmarked to head in Dean Whitehead's inswinging corner.
Darren Carter gave West Brom a lifeline when he hooked in from the edge of the box before Paul Robinson was harshly sent off for a professional foul.
West Brom manager Tony Mowbray:
"Sunderland are a very organised, defensively set up team and you've got to give them credit for that.
"But over the next 10 games I would suggest we will end up with more points than them because of the way we play. We will score more goals than them."
Sunderland manager Roy Keane:
"We had to dig deep after they got a goal out of nothing and then we were under the cosh.
"But the players keep doing that and if you are to get anywhere in life or in football then you have to show those qualities."
West Brom: Kiely, McShane, Clement, Curtis Davies, Robinson, Koumas, Chaplow, Greening (Carter 55), Koren (Gera 55), Kamara, Phillips (MacDonald 55).
Subs Not Used: Daniels, Albrechtsen.
Sent Off: Robinson (87).
Booked: Clement.
Goals: Carter 72.
Sunderland: Ward, Simpson, Evans, Nosworthy, Collins, Edwards (Hysen 41), Whitehead, Yorke (Liam Miller 73), Stokes, Connolly, John (Murphy 62).
Subs Not Used: Fulop, Leadbitter.
Booked: Whitehead.
Goals: Yorke 23, John 49.
Att: 23,252.
Ref: D Gallagher (Oxfordshire).