It was a fortunate escape for the Chiefs who spent nearly 10 minutes with 13 men when both Anton Lienert-Brown and Jacobson were yellow-carded within a minute of each other just before halftime.
Jacobson's offence also led to a penalty try, making it a double hit for the Chiefs. Despite the two-man disadvantage, Damian McKenzie, who set up the opening try for Alex Nankivell, kicked a penalty to take a 10-7 into the break.
With ill-discipline and poor handling letting them down, it wasn't the greatest effort by the Chiefs who flew to Perth after losing the Super Rugby Aotearoa final last Saturday.
It probably seemed fitting the Chiefs were saved by a missed conversion at the end with McKenzie also having an off night from the tee, with three unsuccessful attempts keeping the Force close enough to give them a chance for victory.
The Force, only the second Aussie team to earn a losing bonus point, host the Highlanders in their only other home game next Friday before finishing with a three-game road trip.
Chiefs 20 (Alex Nankivell, Nathan Harris, Jonah Lowe tries, Damian McKenzie pen, con.)
Force 19 (Penalty try, Richard Kahui, Domingo Miotti tries, Miotti con.)
HT: 10-7