The two-time former champion, second behind Sebastian Vettel in last year's race, drove smoothly as he posted a time of 1 minute, 16.265 seconds.
Vettel, who shares the championship lead with Alonso after five races, was ninth quickest and nearly a second slower.
Grosjean, who has made an impressive start to his F1 career — he already has a podium after finishing third in Bahrain and was fourth in Barcelona — clocked 1:16.630.
Perez, who sustained a concussion in a heavy crash last year, posted a time of 1:16.711.
British driver Lewis Hamilton, still seeking his first win of the season, was fourth in 1:16.747, with McLaren teammate Jenson Button in eighth.
The session stopped with just under 10 minutes remaining after Finnish driver Heikki Kovalainen blew his engine and smoke billowed out of his Caterham as he flew through the tunnel section. After the red flag went up, the session did not restart.
He was not the only driver to experience difficulties on the sinewy street circuit, with former champions Kimi Raikkonen and Michael Schumacher both in trouble.
Raikkonen was hampered by suspension problems on his Lotus and failed to post a time after managing only one lap, while the front wing of Schumacher's Mercedes was dented as he flew into a chicane.
Schumacher was 11th fastest.
The seven-time former champion has had a miserable season so far, and has a five-place grid penalty in Monaco.