Cardiff had not won at Torquay for 38 years and it looked initially as if that record would continue.
An error by Bluebirds' goalkeeper Mark Walton allowed Tony Bedeau to give Torquay a 1-0 lead at half-time, but Robert Earnshaw turned the tables after the break.
His first goal came after a brilliant 40-yard solo run on 46 minutes and then two headers, the first from a Danny Gabbidon shot and the second off a Kevin Evans corner, gave the Wales U-21 striker his second hat-trick in a fortnight.
Cork hailed his teenage striker as a "lucky little devil" and again confirmed his desire to keep Earnshaw at Cardiff, despite speculation linking him to other clubs.
Cork maintained his humour on his dug-out dismissal: "I thought the ref was having such a good game I felt I had to say something to him."
Torquay's bad day was made worse when Khalid Chalqi was sent off for throwing a punch, with Paul Brayson sealing the three points for Cardiff with 11 minutes left.
The impressive Bluebirds have now gone 11 games without a defeat since Cork took charge.
Torquay United: Jones, Tully, Herrera, Aggrey, Watson, Ford, Chalqi, Hill, Hockley, Williams, Bedeau.
Subs: Northmore, O'Brien, Rowbotham, Sissoko, Mendy.
Cardiff City: Walton, McCulloch, Gabbidon, Bonner, Evans, Weston, Young, Bowen, Low, Earnshaw, Fortune-West.
Subs: Hallworth, Greene, Collins, Brayson, Nogan.
Referee: P Alcock (Halstead).