Former Arsenal youngster Dasilva broke the deadlock with a moment of real quality when he looked up, picked his spot and coolly curled home into the top corner from the edge of the box.
Brentford looked to have found their feet with the kind of slick passing football that made them such a force last season, pinning the Robins back in their own half for long spells in the first 45 minutes.
Brentford pressed for the opener and on the half hour quicksilver winger Said Benrahma skipped clear of two defenders and flashed a low drive across goal which Ollie Watkins tried in vain to deflect goalwards.
Canos was at the heart of the action again minutes later, his surging run into the box taking out three City defenders only to be thwarted by a desperate Nathan Baker tackle.
The ball dropped kindly for left-back Rico Henry whose curling effort with his weaker right foot sailed agonisingly wide of the right-hand angle.
The defender was in the thick of it again just before the break when his poor clearance fell for Weimann who played in Kasey Palmer whose first-time volley was brilliantly saved by Bees keeper Raya.
That was the Robins' only real foray into the hosts' box in a one-sided first half which saw the visitors happy to soak up pressure and counter at pace.
After the break City had former Brentford keeper Daniel Bentley to thank for keeping them in it, tipping a Christian Norgaard volley over and then reacting quickly to claw a deflected effort out at the near post from the ensuing corner.
But as the game opened up, City had their chances and Josh Brownhill glanced a header just wide when he should have worked the keeper.
Dasilva's strike changed the game and City pressed before a flashpoint in the 81st minute saw Hunt lucky to stay on the pitch after he bundled Canos over the advertising hoardings, the referee deciding a yellow for both was the right outcome.
City's late leveller was harsh on Brentford who took the game to the Robins, but there was still time for Bentley to thwart his former team-mates once more with a reflex fingertip save under the bar to deny Henrik Dalsgaard's deflected cross.