Vettel made a perfect start to his preparations by pipping his teammate Mark Webber by 0.188 seconds.
Vettel, who won the 2011 and 2012 Indian GPs, recorded his best timing of 1:26.683s in just his second lap of the day at the Buddh International Circuit.
The German, who has the chance to clinch his fourth world title this weekend, edged past team-mate Webber (1:26.871s), Mercedes' Nico Rosberg (1:26.899s) and Lotus's Romain Grosjean (1:26.990s) to emerge as the quickest on a hazy morning.
Ferrari's Fernando Alonso is the only other man who still has a chance to win the world championship, but he did not have the best of the start to his preparations as he suffered a gearbox problem. The Spaniard finished 12th fastest, managing just six laps in the morning session.
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However, it was a disappointing opening practice session for Sahara Force India as Adrian Sutil could only manage the 15th position on the time sheet with a best lap of 1:28.468s.
Force India's reserve driver James Calado spun at the tricky Turn Five and could only manage the 18th fastest time.