Home skipper Lee Mansell fired Torquay's third penalty over the bar and the result was decided when Pompey right-back Yassin Moutaouakil successfully converted the visitors' fifth penalty.
Portsmouth had by far the better chances and percentage of possession in a first half they dominated.
Winger Andy Barcham fired a seventh-minute warning shot, saved by home keeper Martin Rice.
Torquay had to scramble clear central-defender Joe Devera's 15th-minute header from the first of a succession of Ricky Holmes corners as Pompey piled on the pressure.
Rice then saved from Sonny Bradley as he sent Holmes' free-kick towards goal on 16 minutes and seconds later Damon Lathrope made a superb goal-line block to keep out Jed Wallace's strike after Bradley invitingly nodded back another Holmes corner.
Torquay's goal led a charmed life with recalled left-back Thomas Cruise somehow managing to keep out Barcham's 80th-minute angled strike, which beat Rice.
The under pressure Gulls finally countered with substitute striker Daniel Sullivan sending keeper John Sullivan full stretch to palm out his shot following Courtney Cameron's lightning break down the right.