Second half goals from Tom Whipp, Dan Richardson and Harry Evans were enough to see John Dent and Gary Pascoe's side claim all three points to significantly ease their relgation fears.
Town had to come from behind to do it, after seeing two first half goals disallowed: the first an Andy Westgarth strike which fell foul of the offside flag, and the second a Rob Wearne tap-in which the referee ruled out for a foul in the build up.
"It was a good performance against a physcial side," said Pascoe. "It's a difficult place to come to, but I thought we worked very hard for it.
"We showed a lot of character to come back from a goal down. When we equalised we looked like the only team who wanted to go on and win it."
Bovey took the lead on the hour mark when Town keeper Danny Burrows' punch dropped to a Bovey forward, whose cross found the head of an unmarked team mate to nod in the opener.
But Town hit back when Whipp's driving run from inside his own half ended with the Falmouth captain finding the back of the net with a curled effort from the edge of the box.
And it got better for Town when, in the 75th minute, Evans and Dominic Batchelor combined well down the left, before Batchelor crossed for Richardson to rifle a shot into the top corner from 18 yards out.
Falmouth were ahead for all of five minutes as Bovey equalised from a poorly defended set piece to set up a tense finish.
Then with five minutes to go Town landed the killer blow when a long ball down the right found Rob Wearne.
The Town striker beat his marker before cutting the ball back for Evans, whose sweetly-struck half-volley found the back of the net.
Eslewhere Town's relegation rivals Cullompton Rangers were thrashed 6-1 away at Camelford, and Liskeard could only manage a 2-2 draw at home against another club struggling for survival, Tavisotck.
Full SWPL premier division results were as follows:
Bovey Tracey 2 - 3 Falmouth Town
Cullompton Rangers 1 - 6 Camelford
Elburton Villa 1 - 6 Exmouth Town
Elmore 1 - 3 St.Blazey
Godolphin Atlantic 2 - 0 Bodmin Town
Ivybridge Town 3 - 2 Newquay
Launceston 4 - 0 Witheridge
Liskeard Athletic 2 - 2 Tavistock
Saltash United 2 - 1 Plymouth Parkway