In front of 5394 fans at HBF Park on Saturday night, the Force levelled the scores at 14-14 in the 49th minute to threaten an upset.
But the Chiefs' class shone brightly from that point on with the visitors scoring the next try and then holding on grimly when Ollie Norris received a yellow card in the 64th minute.
The result leaves the Force (four points) in second-last spot on the table with just one win to show from six games.
The Force's inability to pick up any losing bonus points has also hurt, with just eight more games remaining for them to mount an unlikely finals assault.
"Oh look, our boys will never stop," Force coach Simon Cron said.
"We've played the Brumbies, Chiefs, Blues, Hurricanes, who are all sitting right up there. They'd be four of the best, I reckon.
"And punch for punch, we're in those fights, but we need to make sure we nail those little moments in our game to be able to get the win, get those points."
The Chiefs rose to fifth and improved their record to 4-2.
The rain held off for most of Saturday's match despite Cyclone Narelle having made landfall in Western Australia in recent days.
Former NRL star Zac Lomax warmed up with the Force in a sign his Super Rugby debut could be just one or two weeks away.
The Force put up a huge defensive effort in the first 20 minutes, but when a crack finally did appear Chiefs flanker Luke Jacobson barged through it to score the opener in the 22nd minute.
The Chiefs threatened to score a second try shortly after following a fast break, only for Force scrumhalf Henry Robertson to win a vital penalty at the breakdown.
That momentum shift - which included a line-out steal - proved crucial.
When Ben Donaldson launched a high ball, Force centre George Bridge ran hard to take the grab and set off.
A slice of luck fell Bridge's way when he was tackled, with the ball bobbling backwards to teammate Max Burey who scored a runaway try to level the scores.
The Chiefs hit back in the 39th minute when flyhalf Josh Jacomb rounded Bridge before sprinting 30m to the line, giving the visitors a 14-7 lead.
The scores were back level in the 49th minute when Force skipper Jeremy Williams took the ball from a ruck and moved it forward a few centimetres to score one of his easier tries.
A rolling maul from the Chiefs sent Samisoni Taukei'aho over in the 58th minute and a penalty to Damian McKenzie in the 79th minute sealed the win, with the Chiefs' ability to hold firm when down to 14 men from the 64th to 74th minute proving crucial in the triumph.
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