faster than Webber and almost a second quicker than his time of 1:26.683 in the first session.
Vettel, who has won both previous Indian GP races from pole, can win his fourth straight world title by placing fifth or better on Sunday.
In-form Lotus driver Romain Grosjean was third fastest with a time of 1:26.220, ahead of Mercedes driver Lewis Hamilton in 1:26.399.
"I'm hopeful of another solid day tomorrow which should give us another strong qualifying position if the evidence of today is anything to go by," Grosjean said. "We'll do everything we can to take the fight to Red Bull."
Ferrari driver Fernando Alonso overcame gearbox problems in the morning session to finish the day fifth fastest, ahead of Nico Rosberg's Mercedes and teammate Felipe Massa.
Sebastian Vettel powers his car during second practice session at The Buddh International circuit. (AFP photo)
The second session was marred by handling problems as most drivers came to terms with the smooth, warming track and the softer compound Pirelli tires.
Kimi Raikkonen, who finished 17th in the morning session, appeared to be fighting a losing battle for control of his Lotus and had difficulties taking the tighter turns. He improved to eighth fastest, but looked far from comfortable ahead of Friday's qualifying.
Pastor Maldonado had wheel problems again. The Williams driver who lost a wheel in practice for this month's Japanese GP was forced to park at the entrance to pit lane Friday when he lost a wheel nut and eventually punctured his front right tire after 23 laps of the second session.
Weather at the track was hot and dry, with similar conditions forecast for Sunday.
Vettel signs his autograph for fans as he walks down the F1 paddock at the Indian GP. (AP photo)
"It's hard to say how we will go tomorrow and Sunday, but hopefully we have the pace and can control the race," Webber said. "The car is very consistent, but we need to work on the tires and make sure we get the most out of them."
Tire supplier Pirelli has dropped the more durable hard compound tires for the Indian surface, instead opting for soft and medium options. While the soft tires proved to be considerably faster, drivers complained of a lack of durability.
"The soft tire is not lasting so long here, but it's Friday and the track is still rubbering in," Vettel said. "It's normally improving for Saturday, plus we haven't used this compound for a long time, so tomorrow it should be better."
Alonso had a frustrating start to the first practice, completing only six laps before being forced into the pits with a gearbox issue and ending the morning with the 12th-fastest time. Ferrari repaired the problem in time for the second session, without the need to replace the gearbox.
Mark Webber takes a photo with a fan during the Indian GP at the Buddh International Circuit. (Reuters photo)