A 74th-minute try to centre Byron Ralston and the successful conversion proved decisive after the Force trailed 22-20.
Saturday night's win elevated the Force to eighth, but they will lose that spot even if the ninth-placed Highlanders fall to Melbourne but pick up a bonus point in Sunday's away clash with the Rebels.
It was the Force's first home win of the season.
The eighth-placed qualifying team - either the Force or Highlanders - will play away to the ladder-leading Blues in Auckland in next week's sudden-death quarter-finals.
Needing a final-round win to keep their season going, the Force trailed by 11 points just before halftime.
But they showed enormous heart against the finals-bound Hurricanes, who scored 17 straight first-half points.
The Hurricanes scored four tries to three, with their impressive fullback Josh Moorby crossing for two first-half five-pointers.
It was a rousing final Force game in Perth for coach Tim Sampson - who is being replaced by Simon Cron - and retiring players Richard Kahui, Jeremy Thrush and Greg Holmes.
Centre Kahui was forced off the field with a head knock in the fifth minute and didn't return while fellow former All Black and lock Thrush was sin-binned early in the game for a cynical act.
Captain and halfback Ian Prior kicked two penalties in his 100th game for the Force to give the home side an early 6-0 lead.
Moorby showed great footwork to evade four tackles for his first try and backed up well to score a second, before No.8 Brayden Iose showed tremendous pace to run almost 40 metres to round off a sweeping cross-field move.
Down 17-6, the Force got back into the game just before halftime when Argentinian prop Santiago Medrano crashed his way over and Prior's conversion reduced the deficit to four points at the break.
The Hurricanes were a man short within a minute of the second half starting, with winger Salesi Rayasi sin-binned for an intentional knock on.
The Force twice opted for lineouts rather than shots at goal in the following five minutes and the tactic paid off the second time, with hooker Andrew Ready crashing over from a rolling maul.
Prior's conversion gave the Force a 20-17 lead but a lovely cut-out pass from Moorby set up Rayasi for a try that put the Hurricanes two points up just before the hour.
They had another try scrubbed out for a knock on, but the Force held on and came back to produce the decisive score.
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