The Spaniard set his fastest time on the option tyres towards the end of the session.
Alonso had earlier suffered an off track excursion when he spun on the exit of Turn 2.
The Red Bulls of Sebastian Vettel and Mark Webber finished in second and third, ahead of Lotus's Kimi Raikkonen.
Vettel failed to get a clear run on his option tyres as he firstly encountered Charles Pic and then ran wide at Turn 12.
Lewis Hamilton was fifth but he suffered an apparent left rear suspension failure during the closing moments of the session.
Romain Grosjean finished in sixth place, ahead of the two Force India drivers of Adrian Sutil and Paul di Resta.
As in second practice, neither McLaren driver finished in the top 10, with Jenson Button in twelfth place and Sergio Perez in thirteenth.
Charles Pic was just 2.5s shy of the fastest overall time and was comfortably quicker than Marussia's Jules Bianchi. His team-mate, Max Chilton, managed just seven laps thanks to a KERS issue.