Charles Leclerc was third in the second Ferrari ahead of Mercedes' seven-time champion Lewis Hamilton, defending three-time champion Max Verstappen of Red Bull and Oscar Piastri in the second McLaren.
Norris clocked a best lap of one minute and 24.435 seconds to beat Sainz by 0.328 seconds, but the session was effectively reduced to the final five minutes in earnest on a drying surface.
Pierre Gasly was seventh for Alpine ahead of Valtteri Bottas of Sauber, Sergio Perez in the second Red Bull and George Russell in the second Mercedes.
For the fans, who braved an early storm, the ultimate action was some reward and they also witnessed the rare sight of several drivers spinning off across wet grass - including Verstappen, Bottas and local hope Lance Stroll of Aston Martin.
The circuit was hit by a severe hailstorm before practice began, leaving sections of the track awash with standing water and the pit-lane access closed.
Race Control announced that the session was set to start on time. But with the pit-lane exit closed, this effectively confirmed that no cars could go out to entertain a big Friday crowd braving the elements.
Verstappen, like the rest, remained in the Red Bull garage having admitted he was expecting a difficult weekend as he sought to repeat his triumph from pole position last year.
His chief concern, he said, was not the weather, but his car's performance when riding kerbs on street circuits - a weakness that had accounted for defeats this year in Melbourne, Miami and Monaco.
"This has been a problem since day one of the new regulations," he said. "It's something we know, but we haven't fixed. It takes time. You have to redesign things, it's a work in progress.
"I still think we can do a job this year if it all works out, but at the moment we have to try a few things and see what works. I'm still hopeful."
Scrambling on slippy surface
Marshals worked with drainage machines to clear the track, even as it started raining again, before the action began 25 minutes late with Hamilton - a Montreal specialist, who won his first race in Canada and shares the record of seven wins with Ferrari legend Michael Schumacher - lapping on intermediate tyres.
"Grip level is very low," reported Hamilton, as his former team-mate Bottas joined him on full wets, pitting quickly for a switch to intermediates.
Hamilton's first timed lap was in 1:40.077, some 15 seconds off the anticipated pace, as Norris led a clutch of others out to join him, soon followed by Verstappen, and the sun emerged to help dry the track.
Eleven minutes into the live action, Zhou Guanyu came to a halt after smacking the left side of his Sauber into the wall at Turn Five, bringing out a red flag. "Aquaplaning man, I lost the car," he admitted.
His car was lifted clear, and the session resumed with 21 minutes remaining and the newly-resurfaced circuit drying rapidly.
The improving conditions brought tumbling lap times. Hamilton set the pace, followed by Leclerc and then Sainz, in 1:27.485, all on intermediates before the teams opted to preserve their tyres in expectation of a wet second session later Friday.
With five minutes to go, Leclerc went out on soft 'slicks' followed by Norris, Verstappen and Sainz, all scrambling to stay on the emerging dry line in a frantic finale.
