The Old Trafford outfit were still trying to adjust to a line-up with only one conventional winger in Ashley Young when Keith Andrews slid in to reach Liam Ridgewell's low left-wing cross, but prodded his effort wide.
Together with skipper Patrice Evra, Young tormented the right side of West Brom's defence.
The former Aston Villa man had a shot beaten away by Ben Foster, then ran on to Danny Welbeck's back-heeled through ball before cutting a cute cross back into the box which Jonas Olsson managed to scramble away.
United finally took the lead on the half-hour mark when Rooney touched home Javier Hernandez's cross.
Booked at the start of the second period for a foul on Rooney, Olsson brought his afternoon to an early conclusion when he was beaten to Welbeck's pass by Hernandez and chopped the Mexican down instead. And within five minutes, the hosts had their second, Rooney again the scorer, slotting home a clinical penalty after Andrews had fouled Young.