Red Bull's 25-year-old German, who leads Alonso by six points with four races remaining, continued to gather momentum as he limbered up for what could be a fourth win in succession on Sunday.
Winner of last year's inaugural race at the hot and hazy Buddh International Circuit south of New Delhi, where the double world champion set a best time of one minute 27.619 seconds in the morning and 1:26.221 in the afternoon.
The latter time was comfortably inside his race lap record of 1:27.249.
"It was dusty to start and improved lap by lap so I wouldn't be surprised if tomorrow the order is different," said Vettel. "But we've had worse Fridays so I'm happy."
McLaren's Jenson Button was second fastest before lunch, 0.310 slower, while Vettel's Australian team mate Mark Webber anchored a Red Bull one-two in the later session. Alonso was third in both.
"The track conditions, which change rapidly lap after lap, make it even more complicated to understand the situation relating to the hierarchy down the pit lane," said the Spaniard, who had a problem-free day.
Button had a gearshift problem in the afternoon, two laps into a long run on heavy fuel, and struggled to get the tyres to work as he wanted.
"I'm not sure our race pace is that good actually," the 2009 champion said. "Over one lap I think there's quite a bit of work to do, I think we're just struggling for general grip."
The top three in first practice were in the same order as last year's podium finishers at the inaugural Indian Grand Prix, which Vettel dominated after having already clinched his second championship.
McLaren's Lewis Hamilton was fourth and sixth on the timesheets and more positive than his team mate after being told from the pit wall that he was "the fastest guy on high fuel".
Kimi Raikkonen, third in the championship with Lotus, improved from 10th to fifth fastest on his first day on the track. Last year's race was before he began his comeback after two seasons' absence.
The team again used their new 'Coanda' exhaust system.
Alonso's Brazilian team mate Felipe Massa had two spins in the afternoon with Ferrari saying the car's balance had been compromised by an incorrect setting.
Mexican Esteban Gutierrez replaced compatriot Sergio Perez at Sauber for the first session, after the regular race driver was reported to be unwell, and was 20th. Perez returned for the afternoon, looking far from sickly.
Gutierrez is widely expected to replace Perez next season, with the older Mexican moving to McLaren to take over from Hamilton when he goes to Mercedes.
With the little-used track dusty at the outset, teams took their time to progress beyond installation laps in the morning and then focused on gathering data and testing updates before tyre work in the afternoon.
Ferrari, whose wind tunnel data has let them down this season, were trying out updated rear and front wings in the morning and focusing on tyre comparisons in the afternoon. Team boss Stefano Domenicali said it was still too early to say whether the updates would make a significant difference.
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