Cavanagh smashed home a 20-yard free-kick to send a bumper 4,000 strong crowd wild with delight in blustery East Lancashire.
It had looked as if Stanley would fail to take advantage of Lee Mansell's straight red card for tripping Shaun Whalley in the 55th minute.
But defender and captain Cavanagh, playing his first full game after knee surgery, delighted the 4,000 strong Fraser Eagle Stadium crowd - all who had been let in for free.
Stanley estimated it would cost them in the region of £15,000 to let their fans in for nothing to cheer on their side in what they billed as their biggest game ever.
But what they lost in revenue, they could make up with the prize of Football League survival come the end of the season in May.
Torquay are now completely cut adrift at the foot of League Two, and will literally need a miracle to preserve their own league status.
Just before Cavanagh's moment of glory, Stanley boss John Coleman was sent to the stands for arguing with the fourth official. But he will not care one jot, as his side won their first game in seven, while also keeping a clean sheet for the first time in almost 30 games.
After the game, Torquay head coach Keith Curle locked his side in the dressing room for almost an hour and a half.