The victory saw the Bloemfontein-based side climb from the bottom rung of the ladder, moving into fourth position, with Griquas dropping to fifth in the standings, just above the Blue Bulls.
The Cheetahs got on the scoreboard first when the pressure they heaped on Griquas led to prop Ross Geldenhuys' five-pointer.
Winger Nico Scheepers converted to give the home side the early lead.
From the resultant kick-off it all turned a little helter skelter with both teams squandering opportunities due to passes not going to hand.
The visitors finally got on the scoreboard in the 20th minute after flyhalf Francois Brummer kicked a much needed penalty.
A yellow card to Griquas fullback Willie le Roux for a professional foul saw the visitors one man short and the Cheetahs exploited the advantage.
Centre and captain Robert Ebersohn dotted down under the crossbar after the Peacock Blues failed to patch the holes in their defence, and Scheepers converted.
Le Roux's absence left the visitors in disarray and the Cheetahs surged ahead on attack.
They set up camp on Griquas' goal line and the immense pressure caused the visitors to infringe at the breakdown.
Scheepers kicked a penalty 10 minutes before half-time to give his side a comfortable 17-3 lead.
Griquas looked down and out and not even a second penalty by Brummer to close the deficit seemed enough to lift the Kimberley-based side out of their rut. They lacked consistency on defence and earned little possession in the first 40 minutes.
They came out, however, with much more prowess and put the Cheetahs under pressure in the first five minutes of the second period.
The home side's defensive structures were up to the challenge, though, and Griquas were left wanting.
A decision to kick for touch rather than goal came off for the visitors when flanker Marnus Schoeman burst over from a rolling maul. Brummer converted to bring Griquas within four points and left the Cheetahs to regroup.
The hosts put some daylight between themselves and Griquas when Scheepers kicked another penalty, but winger Jannie Boshoff dived over in the corner after some good attacking play by the Griquas loose forwards. Brummer converted to level the scores.
Some attractive rugby from both sides followed, but defence was air tight.
Griquas again infringed and got penalised, with Scheepers kicking the penalty with ease.
And fullback Hennie Daniller went over in the corner after the Cheetahs put together some attacking phases of play, with Scheepers again converting.
Winger Raymond Rhule added a bonus-point try as the Cheetahs picked up their first win in four games.
Teams:
Free State Cheetahs:
15
Hennie Daniller, 14 Nico Scheepers, 13 Raymond Rhule, 12 Robert
Ebersohn (captain), 11 Rayno Benjamin, 10 Sias Ebersohn, 9 Sarel
Pretorius, 8 Philip van der Walt, 7 Lappies Labuschagne, 6 Heinrich
Brüssow, 5 Izak van der Westhuizen, 4 Francois Uys, 3 Ross Geldenhuys, 2
Hercu Liebenberg, 1 Marcel van der Merwe.
Substitutes: 16 AJ le Roux, 17 Brummer Badenhorst, 18 Carl Wegner, 19 Hendro Scholtz, 20 Tewis de Bruyn, 21 Philip Snyman, 22 Andries Strauss.
Griquas:
Substitutes: 16 Matt Dobson, 17 Ivann Espag, 18 Edwin Hewitt, 19 Justin Downey, 20 Jacques Coetzee, 21 Marnitz Boshoff, 22 JP Nel