Championship leader Leeds United was held to a 1-1 draw by Luton Town on Wednesday (AEST) and the Baggies closed the gap to just one point with a 3-0 victory at Hillsborough.
Charlie Austin's first-half penalty was added to by a brace from Pereira after the break as Slaven Bilic's side restored their five-point cushion in the final automatic promotion place.
The play-off places are what Derby and Preston are chasing and it was the Rams who came out on top at Deepdale thanks to Rooney.
England's all-time leading scorer found the net with a first-half free-kick to leave Derby one point behind sixth-placed Cardiff City.
Nottingham Forest, which Derby faces next, strengthened its grip on one of the play-off berths, Tiago Silva scoring the only goal in 1 -0 victory over Bristol City.
At the other end of the table, Huddersfield Town climbed out of the relegation places with a 3-0 success at Birmingham City.
Karlan Grant, Fraizer Campbell and Elias Kachunga scored the goals for the Terriers, who were replaced in the bottom three by Hull City.