Bury could only muster a single reply from Nathan Cameron as they slipped to within two points of the relegation places.
Torquay capitalised on sloppy defending to open the scoring after 18 minutes as Downes bundled the ball home from Kevin Nicholson's deep corner.
The Shakers equalised in the 24th minute when their central defenders found themselves in an unfamiliar attacking position, with William Edjenguele laying the ball off for Cameron to slam home.
But the visitors replicated a successful formula to go back in front just before the half-hour mark as this time McCallum headed home Nicholson's corner at the far post.
Goalkeeper Martin Rice preserved Torquay's lead by tipping the ball acrobatically round the post after Cameron had got his head to a mishit shot from Andy Procter.
Chris Sedgwick did find the net directly from a corner but it was ruled out for a foul on Rice.
Torquay rounded off their win in the 57th minute, McCallum finding the top corner of the net from Elliot Benyon's cutback.
- Sports & Recreation
- Nathan Cameron
- Aaron Downes
- Paul McCallum