The Lotus driver surged to the top of the times six minutes from the end of the session, his best of 1m20.730s coming during a flurry of quick times set on the soft tyre inside the final 10 minutes.
Fernando Alonso was second for Ferrari, ahead of McLaren's Sergio Perez, who ended up in the barriers with just minutes remaining after spinning at speed on the approach to Turn 11.
Having set the pace during the first two practice sessions, Sebastian Vettel was just fourth fastest in free practice three.
The Red Bull driver spent the majority of the session working on a long run on the medium tyre, and was sitting 19th before improving with a soft tyre run right at the end.
Felipe Massa was fifth, slotting in ahead of Lewis Hamilton, Mark Webber, Nico Rosberg, Jenson Button and Adrian Sutil.
Kimi Raikkonen missed out on a top 10 spot, finishing 11th after complaining about a lack of rear grip.
Grosjean's pace was not limited to the soft tyre. Earlier in the session, he was one of the pacesetters on the medium tyre, going fastest 18 minutes into the session.
But in the end it was Hamilton who led the way on the medium tyre.
He first jumped to the top 26 minutes into the session with a 1m22.266s, before lowering his best time to a 1m21.942s, the fastest that was set on the harder of the two compounds.