The Force entered Saturday night's match knowing only a bonus-point win would be enough to keep their faint finals chances alive, while the Drua's hopes were already extinguished following Queensland's last-gasp win over Moana Pasifika earlier in the day.
Zac Lomax's 69th-minute try from what looked to be an obvious forward pass put the Force ahead, but the home side needed another two tries from there to snare the winning bonus point.
Captain Jeremy Williams looked to have given the Force hope when he touched down in the 78th minute, but the TMO rubbed it out after deeming there had been an earlier knock-on.
The Force desperately tried to get another try to keep the bonus point in play, but it wasn't to be.
The result means the Force are six points adrift of the sixth-placed Reds with only one round remaining.
Force players looked dejected after the win, knowing their late-season charge hasn't been enough to snare the franchise a maiden finals berth.
"It's really bittersweet," Force captain Jeremy Williams said.
"Obviously really happy to get the win ... but at the same time it's shattering, because you know something you've worked so hard for all year gets taken away from you.
"Like, you're stoked to get the win, but is the team song going to be all that energetic today? It's going to be a weird vibe."
Carlo Tizzano's 10th-minute try from a rolling maul gave the Force the perfect start.
The visitors levelled in the 17th minute when Kitione Salawa barged over, and they were ahead when hooker Zuriel Togiatama found himself free in the corner.
Fijian Drua had more metres gained, more carries and more clean breaks in the first half, and deserved their 12-7 lead at the break.
The Force obliterated Drua's scrum against the feed in the 48th minute, and the home side produced another dominant scrum a few minutes later for No.8 Vaiolini Ekuasi to bust over.
Kurtley Beale entered the fray in the 54th minute to notch appearance No.186 in Super Rugby, putting him into outright third on the all-time games list.
Despite having a man in the sin bin, Drua were able to regain the lead via a penalty, but Lomax put the Force back in front when he touched over in the corner.
Mac Grealy's pass to Lomax looked forward, but the try still stood.
"I think it was a forward pass into a try. I think everyone else thought that," Drua coach Glen Jackson said.
Drua captain Temo Mayanavanua added: "(We are) all human beings, at the end of the day, we all make mistakes. It's important that we just move forward."
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