The Chiefs led by 10 points after Aaron Cruden slotted his fifth penalty goal three minutes into the second half, but the defending champions were scoreless thereafter as the Force staged a late rally.
Force winger Pat Dellit scored a brace of tries, his second bringing the Perth-based team within a point early in the final quarter, but the Australians went a man down for the last 10 minutes and were unable to conjure up a winning score.
The victory gave the Chiefs breathing space at the top of the New Zealand conference with seven rounds left in the southern hemisphere competition, but left their captain Craig Clarke slightly disappointed.
"It's a win. Pretty frustrating," the lock said in a pitchside interview.
"Again we've made a few errors. I know it's wet, but it's pretty disappointing."
The narrow loss was further heartbreak for the Force, who have managed only two wins and a draw this season, despite being competitive in most of their matches.
The Perth strugglers made the brighter start, with Dellit touching down in the fourth minute after kicking forward a loose ball off the ground out wide and collecting it after a quick sprint to the line.
Big Chiefs lock Brodie Retallick set up his team's sole try in the 16th minute, dishing off to winger Lelia Masaga, who shrugged off a couple of weak tackles before crossing in the right corner.
The game was then taken over by the match official, with Cruden and Force full-back Brendan Hayward trading penalty goals.
Hayward put the Force within eight points 18 minutes into the second half with his third kick before the Force's wingers combined for the team's second try.
Shaggy-haired winger Nick Cummins made a break on the left flank before being brought down a few metres shy of the line.
The Force spread the ball to the right and quickly back again, with South African fly-half Sias Ebersohn dishing off to Dellit for a trouble-free run over the line in the left corner.
Hayward's conversion trimmed the lead to a point but the Chiefs drove forward and bullied the Force scrum deep in their 22.
With the turf being reduced to tatters, the Force forwards collapsed repeatedly, leading to referee Mike Fraser losing patience and sending prop Kieran Longbottom to the sin-bin for collapsing.
Although the Force survived the assault, with Chiefs flanker Liam Messam losing the ball forward in a dart to the line, they were unable to score again and surrendered the match when Ebersohn surprisingly kicked the ball into touch in the final minute.