Vettel's Formula 1 world championship rival Fernando Alonso was back in eighth, although he abandoned his final run due to traffic.
Most of the session's action was compressed into the final 10 minutes when the field went into qualifying simulation mode.
Prior to that, the two Mercedes had exchanged the top spot initially before Button set a 1m13.917s that would keep him in first place for most of the morning. Red Bull driver Vettel got within 0.007s of the McLaren but could not depose it.
The Force Indias were the first to show their hand on medium tyres, with first Nico Hulkenberg, then Paul di Resta grabbing first before Button snatched it back almost immediately, the position changing hands three times in less than a minute.
Button's 1m13.192s proved unbeatable for all bar the Briton himself, who got down to a 1m13.188s with his next attempt, despite a disappointing middle sector.
No one could get closer than two tenths adrift of that pace until Vettel delivered a 1m13.245s lap after the chequered flag, vaulting him up from 10th to second.
His team-mate Mark Webber took third, just ahead of the second McLaren of Lewis Hamilton.
Romain Grosjean was a frontrunner all morning, eventually securing the final top-five slot for Lotus.
Force India's burst of pace was no fluke, as di Resta and Hulkenberg retained sixth and seventh even after all the frontrunners had done medium-tyre runs.
The Ferraris had to settle for eighth and 10th, Alonso and Felipe Massa split by the Williams of Pastor Maldonado.
Kimi Raikkonen got no useful running at all. His Lotus suffered a Renault engine failure on the second straight as he went onto what would have been his first flying lap 15 minutes into the morning. Lotus will be able to fit a used spare for the race without having to take a penalty for requiring a ninth engine.
In his final F1 practice session, Michael Schumacher had a lucky escape when Bruno Senna ran very wide out of Juncao and spun his Williams back across the straight in the Mercedes' path. Schumacher avoided being collected and continued safely.
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