Giteau put the Force up 3-0 with a penalty in the ninth minute, and inside centre James O'Connor, on a pass from Giteau, scored the home side's only try in the 31st minute. Giteau's conversion gave the Force a 10-0 lead.
Winger Danwel Demas scored for the Cheetahs five minutes later after kicking ahead and taking advantage of a perfect bounce back to him to score. Jacques-Louis Potgieter kicked the conversion and Giteau added a penalty in the 39th minute to give the Force a 13-7 halftime lead.
Five minutes into the second half, Giteau kicked a drop goal to give the Force a nine-point lead, but Potgieter narrowed the margin to 16-10 with a penalty in the 61st to complete the scoring.
Both teams had to contend with unusually hot nighttime conditions at Subiaco Oval, and the Force seemed to cope better than the visitors.
"For a while there I thought we were playing in Durban," Cheetahs captain Juan Smith said of the heat.
"It's a disappointing result. We didn't get the points on the board when we needed to."
Force captain Nathan Sharpe said his team wasn't concerned by the slow scoring in the second half when each side managed just three points each.
"We weren't worried about how many points were on the scoreboard," Sharpe said. "We knew we just needed to keep the pressure on them."
The win evened the Force's record at 1-1 while the Cheetahs are 0-2, but have picked up bonus points in each of their losses for losing by fewer than seven points. They lost by six points to the Lions at Johannesburg last weekend.
ScorersForce: Try - James O'Connor. Conversion - Matt Giteau. Penalties - Giteau (2). Dropped goal - Giteau
Cheetahs: Try - Danwell Demas. Conversion - Jacques-Louis Potgieter. Penalty - Potgieter