Chile striker Brereton Diaz took his tally for the season to seven with a first-half penalty and a close-range finish after the break before Sammie Szmodics added the third.
The victory put Rovers just outside the play-off places on goal difference, leaving new Millers boss Matt Taylor still looking for his maiden win following the midweek home draw with Millwall in his first game.
Rovers have now won seven of their Championship games but lost six in an up-and-down campaign.
Each of their last four league wins have been followed by a defeat, a sequence Tomasson will hope they can break when they go to local rivals Wigan on Tuesday.
The Millers were the more threatening team in the early stages with Oliver Rathbone seeing his curling effort tipped away by Rovers keeper Thomas Kaminsky and Tom Eaves striking a post with a shot.
Rotherham have not scored often on the road this season and that trend continued in Lancashire.
Here’s how every Rotherham player rated from the game, based on WhoScored analysis...
