Target man Jon Parkin put Fleetwood 1-0 ahead against the run of play in the 25th minute with a superb far post looping header to greet left back Dean Howell's deep cross from the left.
It was top scorer Parkin's ninth goal of the season and third in as many matches following a lengthy lay-off with a hamstring problem
Injury struck the veteran again and he was replaced in attack before half-time by Jean-Michel Fontaine, who had an early second half effort ruled out.
However it was Davies who shone, making a brilliant fifth minute diving save to beat out recalled Ashley Yeoman's thumping shot.
Torquay had penalty appeals waved away as Ryan Jarvis' rising follow-up shot from the edge of the box crashed off a defender's arm.
Davies made two saves to deny Wales Under 21 international Billy Bodin in quick succession and when Kevin Nicholson eventually beat the keeper, Howell was on the goal-line to clear.
It was a similar story in the second half as Torquay poured forward in search of a leveller and Davies made a fine save to keep out Kevin Nicholson's goal-bound long range strike.
United central defender Aaron Downes smashed a header off the Fleetwood crossbar in stoppage time.