Baggies bounce straight back
The result meant the Baggies, relegated last May after a season in the top flight, joined Championship leaders Newcastle United in making sure of the two automatic promotion slots.
The visitors were in party mood by half time, with Graham Dorrans putting them 1-0 up against the run of play from a free-kick in the 31st minute and Chris Brunt doubling the scoreline seconds before the break at the Keepmoat stadium.
Jay Emmanuel-Thomas pulled a goal back two minutes after the restart before Roman Bednar made it 3-1 with a header in the 73rd but the visitors had a nervous final five minutes after James Hayter again narrowed the gap.
West Brom, managed by former Italy midfielder Roberto Di Matteo, have been promoted four times in the last nine seasons.
They have 86 points from 43 matches, six adrift of Newcastle.
Eleven points behind them in third place, former European Cup winners Nottingham Forest made sure of a promotion play-off slot by beating Ipswich 3-0 at home.