Amid all the focus on his team-mate Kimi Raikkonen's relationship with the squad, Grosjean bucked the usual Friday morning trend by waiting until the closing moments to set his best time.
Grosjean's 1m44.241s lap put him 0.192 seconds clear of Lewis Hamilton, who would normally have expected to stay up front after winning the traditional mid-session dice for top spot.
No one set a flying lap for the first half hour, and it was near the hour mark before the Mercedes and Red Bulls really raised the bar.
Hamilton emerged on top for Mercedes at that stage, 0.066s ahead of Sebastian Vettel's Red Bull.
The world champion had a slight scare at the end of the session, when he misjudged his entry to the Red Bull pit stall and required some evasive action from his crew as he locked up.
Vettel's team-mate Mark Webber beat Nico Rosberg's Mercedes to fifth, with the in-the-spotlight Raikkonen seventh.
Paul di Resta put Force India in an encouraging seventh place. His team-mate Adrian Sutil moved aside for James Calado this time. The GP2 title contender was 14th.
Other 'Friday drivers' in action were Caterham's Heikki Kovalainen and Marussia's Rodolfo Gonzalez, who were 20th and 22nd.
The McLarens ended up eighth and 10th, split by the Williams of Pastor Maldonado.
Ferrari had a low-key start, with Fernando Alonso and Felipe Massa 12th and 17th.