Neither side are in contention for finals qualification, meaning only pride was at stake at the Newlands Stadium.
The Stormers were expected to welcome back captain Jean de Villiers from injury, but the 33-year-old centre was a late withdrawal, meaning Van Wyk was named in the starting XV, while Schalk Burger was made skipper on his own return to the side.
There was no sign the Cape Town-based team were missing their influential leader, however, as they dominated from the start, opening the scoring after winning a line-out and driving Fourie over the try line in the fifth minute.
The Cheetahs did manage to threaten on occasion but their hopes of drawing level were undermined by Adriaan Strauss being sent to the sin bin for a tip tackle on Van Wyk midway through the first half.
Coleman slotted home a penalty soon after and added the conversion after Van Wyk finished a flowing, counter-attack from the Stormers, which started inside their own 22.
After the interval, Coleman and Grant notched three-pointers when the Cheetahs were penalised for infringements at the ruck to give the Stormers a 21-point cushion.
With 10 minutes remaining, Kolisi dived over behind the posts for his side's third try and although the home side finished with 10 men after Michael Rhodes was yellow carded for pulling the hair of Cheetahs replacement Hilton Lobberts, it mattered little to the overall result.
Indeed, the Stormers increased their lead before the full-time whistle as Tagicakibau put the final flourish on proceedings after grounding the ball from Grant's chip kick.