It had been Hamilton who had set the pace early on when teams were looking for lap times, but Alonso surged ahead with a 1m 17.238s - little more than one hundredth of a second faster than the Briton.
Hamilton responded by setting new outright bests in the first and second sectors, but had a massive lock-up at the Turn 10 hairpin and abandoned his lap, pulling straight into the pits at the same time as Alonso.
With the field switching focus to long runs in the final minutes, Alonso therefore ended on top, with Hamilton second and 0.016s adrift after a lap of 1m 17.254s.
Nico Rosberg meanwhile rounded out an incredibly tight top three with 1m 17.384s, little more than one tenth of a second down on his Mercedes team mate.
There was then a jump to fourth, which was claimed by Red Bull's Sebastian Vettel with 1m 18.131s. He was followed by Valtteri Bottas's Williams on 1m 18.361s, a late-improving Daniel Ricciardo on 1m 18.435s int he second Red Bull, the McLarens of Jenson Button and Kevin Magnussen - a Circuit Gilles-Villeneuve rookie - on 1m 18.446s and 1m 18.514s respectively, Kimi Raikkonen on 1m 18.578s, Jean-Eric Vergne on 1m 18.643s, and the Force Indias of Nico Hulkenberg and Sergio Perez on 1m 18.733s and 1m 18.959s respectively.
Eight tenths of a second therefore covered fourth through to 12th.
Adrian Sutil was 13th for Sauber with 1m 19.108s, narrowly ahead of Romain Grosjean's Lotus on 1m 19.142s and Daniil Kvyat's Toro Rosso on 1m 19.177s. Lotus's Pastor Maldonado then headed Williams' Felipe Massa, 1m 19.340s to 1m 19.575s as Esteban Gutierrez lapped his Sauber in 1m 19.804s.
Marussia had hoped to get ahead of the Saubers here but Jules Bianchi's best was 1m 20.200s as team mate Max Chilton managed 1m 20.844s. They were comfortably ahead of the Caterhams, as Marcus Ericsson's 1m 21.404s narrowly beat Alexander Rossi's 1m 21.757s. The American will hand the CT05 back to Kamui Kobayashi for FP2.
A number of drivers had off-track incidents during the 90-minute session, most notably Bianchi, who tagged the wall exiting Turn 4 and limped back to the garage. The resulting damage ended his session prematurely.
While Ferrari entered the weekend hopeful of improvements, the real truth about the team's underlying pace - and that of rivals Mercedes - will emerge more in FP2 and of course qualifying, when everyone runs the same fuel loads.
The indications however are that Mercedes might just have a challenge on their hands this weekend.