Tony Bedeau gave the visitors a welcome seventh minute lead, before substitute Adam Le Fondre equalised for the home side in the 64th minute.
Both goalkeepers made a string of excellent saves to keep the scoreline as it stayed, particularly Torquay shot-stopper Andy Marriott.
But a point was enough for County to move off the bottom of the table with fellow strugglers Rushden & Diamonds not playing tonight.
Stockport could have scored as early as the third minute through Keith Briggs, but the midfielder, who chased down a long-ball from Ashley Williams, saw his shot saved by Marriott.
And to further frustrate the home side, Torquay then went and took the lead four minutes later.
Bedeau had acres of space to head past Stockport keeper James Spencer after a pinpoint cross from Darren Garner.
Williams should have levelled for County in the 13th minute, but fellow defender Rob Clare took the ball away from him just as he was about to head home, unmarked at the back post.
Gannon's men pressed and after a wonderful through-ball from Tes Bramble, Briggs only had Marriott to beat.
But the former club captain fired into the sidenetting when he should have done much better.
At the other end Martin Phillips forced to make a good save, before Anthony Lloyd fired straight into the arms of Spencer after County failed to clear their lines.
Damien Allen could not beat Marriott with a close-range volley nine minutes before the break, while defender Michael Raynes limped off with a hamstring injury on the stroke of half-time.
He did not return after the resumption. Yet another worry for Gannon in troubled times at Edgeley Park, albeit County's form as turned around recently.
Bramble nearly equalised in the 56th minute, but his side-footed volley from the edge of the six-yard box did not trouble Marriott.
But the equaliser came ten minutes later when substitute Le Fondre, on as a first-half replacement, broke free to poke home Matthew Hamshaw's cross at the near post.
Garner fired high and wide in the 70th minute as Torquay looked to re-establish their lead, while Hamshaw forced Marriott into making a good low save as County rallied.
Gannon introduced new loan signing Michael Symes in the 75th minute, but try as they might County could not find a winner to alleviate their relegation worries.
Striker Symes has arrived at Edgeley Park on a one-month loan deal from Bradford City, but given a quarter of an hour to play with, the youngster was not able to make his mark on the match.
Mickael Wolski found Hamshaw with a delicious pass in the 84th minute, but Marriott produced a wonderful save after the midfielder unleashed a firecracker at him.
A minute later Spencer made a brilliant save from sub Matt Hewlett. Both sides were desperate for full points, but there were no more goals to come.