Massa's time of 1:34.487 was almost a tenth of a second quicker than team-mate Fernando Alonso.
The first 30 minutes of the session was relatively quiet as teams opted to stay in the garage due to dusty track conditions. Once running got under way, drivers opted to use the hard compound tyre.
Nico Rosberg was third for Mercedes, ahead of reigning world champion Sebastian Vettel.
Paul di Resta was fifth, with compatriot Jenson Button in sixth place. Mark Webber and Adrian Sutil were seventh and eighth, with the Lotus drivers Kimi Raikkonen and Romain Grosjean rounding out the top ten. Grosjean suffered from a KERS issue during the session, but team principal Eric Boullier confirmed that the problem was swiftly fixed.
Heikki Kovalainen returned to an F1 car for the first time since last year's Brazilian Grand Prix and he finished 0.6s down on team-mate Charles Pic. Venezuelan driver Rodolfo Gonzalez made his debut at a race weekend, finishing bottom of the time sheets as his practice run was compromised by a gearbox problem.