The result lifted the Cheetahs to 26 log points and moved them into 10th position, while the Force's woes continued after picking up only two wins in 10 outings.
The absence of injured flyhalf Johan Goosen was noticable as his replacement, Sias Ebersohn, struggled to get the hosts on the front foot.
The Cheetahs had a rocketing start but they lost energy as both sides lacked any real composure for the better part of the first half.
The Bloemfontein side had an early opportunity to open the scoring with a penalty, after they had the Force in all sorts of trouble on the attack.
Ebersohn, however, could not convert, and the Force put the first points on the board with flyhalf David Harvey slotting a penalty in the eighth minute.
Harvey and Ebersohn then engaged in some aerial ping-pong before the latter made a confident break and slotted the penalty from the resulting infringement at the breakdown by the visitors.
The tourists were organised on defence and seemed satisfied to be conceding penalties rather than tries, with Ebersohn slotting his second after the Force again snatched possession on the ground.
While they did not see as much of the ball in the first 40 minutes, the Force got some points when Harvey slotted a penalty in the dying stages of the first half.
Tewis de Bruyn followed suit to give the Cheetahs a 9-6 lead at the break.
Cheetahs coach Naka Drotske sent out scrumhalf Piet van Zyl and loose forward Ashley Johnson for the second stanza, with the latter providing some extra force at the breakdown.
The home side got stuck on their goal-line in the 46th minute and Force centre Winston Stanley scored a converted try after charging down Cheetahs full-back Hennie Daniller's clearing kick.
Hitting back, though, Cheetahs captain Adriaan Strauss scored in the corner eight minutes later.
Ebersohn missed with the conversion, leaving his side one-point ahead.
The flyhalf slotted one more penalty, with a little more than half an hour left on the clock, to secure the win.
Ebersohn had another shot at goal with five minutes remaining, but again he missed.
Teams:
Cheetahs:
15 Hennie Daniller, 14 Cameron Jacobs, 13 Robert Ebersohn, 12 Andries Strauss, 11 Willie le Roux, 10 Sias Ebersohn, 9 Tewis de Bruyn, 8 Philip van der Walt, 7 Justin Downey, 6 Heinrich Brussow, 5 Izak van der Westhuizen, 4 George Earle, 3 WP Nel, 2 Adriaan Strauss (captain), 1 Coenie Oosthuizen
Substitutes: 16 Hercu Liebenberg, 17 Trevor Nyakane, 18 Andries Ferreira, 19 Ashley Johnson, 20 Piet van Zyl, 21 Riaan Smit, 22 Philip Snyman
Force:15. Alifeleti Mafi, 14. Samu Wara, 13. Nick Cummins, 12. Winston Stanley, 11. Napolioni Nalaga, 10. David Harvey, 9. Brett Sheehan, 8. Matthew Hodgson, 7. David Pocock (captain), 6. Richard Brown, 5. Nathan Sharpe, 4. Toby Lynn, 3. Salesi Ma'afu, 2. Nathan Charles, 1. Pekahou Cowan
Substitutes: 16. Elvis Taione, 17. Salesi Manu, 18. Phoenix Battye, 19. Locky McCaffrey, 20. Josh Holmes, 21. Ben Seymour, 22. Rory Sidey