Substitute Jutkiewicz, who is moving to Everton for £750,000 in the summer, was picked out by fellow substitute Aaron Brown and he blasted the ball home left-footed from the edge of the penalty area.
Torquay had only equalised a minute before with captain Lee Peacock stroking home the penalty after Peacock fouled midfielder Matt Hockley.
Swindon took the lead in only the second minute through manager Paul Sturrock's son Blair Sturrock. Torquay defender Lee Andrews' hapless back header let in striker Sturrock who calmly lobbed Simon Rayner in the Torquay goal from 16 yards.
Swindon should have doubled their lead on 63 minutes, but they missed a penalty.
Dean Gordon brought down Swindon striker Barry Corr with a clumsy challenge in the box. Jack Smith stepped up to take the spot kick but saw his shot brilliantly pushed around the post by Canadian Rayner in the Torquay goal.
This was Torquay's 15th away loss this season and they now face a real battle to beat the drop after not winning away since September.
Torquay pushed forward desperately trying to get back in the game and substitute Chris McPhee missed a glorious chance to level. The former Swindon man was picked out from Lee Mansell's corner, but he put his free header high and wide over the Robins' goal.
Swindon missed a chance to wrap up the victory when Jutkiewicz played in Corr but his snapshot from 15 yards was well saved by man-of-the-match Rayner in the Torquay goal.