Doncaster make two changes from the side that drew at Reading on Saturday, Billy Sharp and Wade Fairhurst started for the first time in a Rovers shirt.
The pair replaced the injured James Hayter and James Coppinger.
The duo made a dream start when Sharp`s cross dissected the Albion defence and Fairhurst tapped in, inside the first ten minutes to score his first senior goal for the club.
West Brom equalised when Olsson equalised with a header from a corner, Oster who was stood by the near post would have been disappointed the ball got past him and into the net.
Rovers were forced into a substitution soon afterwards when James O`Connor replaced Gareth Roberts in defence.
Rovers hadn`t been overawed by their highflying opponents in the first half and deservedly went in level at half time.
Olsson scored his second goal to give West Brom the lead half way through the second half when he stooped down to score with another header.
Lockwood had a great chance to equalise late on when he had a free header inside the box but his effort went over.
West Brom wrapped up the game with five minutes remaining when substitute Wood hit a cracking volley to give Sullivan no chance from 25 yards out.
The Baggies returned to the top of the Championship, Rovers can take plenty of positives in defeat after a spirited performance.
Carson, Zuiverloon, Martis, Olsson, Mattock, Brunt (Wood 71), Koren, Mulumba, Dorrans, Cech (Thomas 11), Bednar (Teixera 90)
Subs not used
Kiely, Cox, Reid, Barnett,
Sullivan, Roberts (O`Connor 32), Shackell, Lockwood, Chambers, Woods, Stock (Wilson 76), Spicer, Fairhurst, Sharp, Oster (Shiels 62)
Subs not used
Smith, Hird, Fortune, Webster,
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