Vettel recorded 1 minute, 26.683 seconds for a lap of the Buddh International Circuit, just .188 faster than fierce rival Webber.
Vettel, who has won both previous Indian GP races from pole, can seal his fourth straight world title by placing fifth or better on Sunday.
The increasingly competitive Nico Rosberg was third fastest in a Mercedes with 1:26.899, ahead of in-form Lotus driver Romain Grosjean in 1:26.990.
Mercedes' Lewis Hamilton posted the fifth fastest time, with McLaren's Jenson Button sixth and Felipe Massa seventh.
Massa's Ferrari teammate Fernando Alonso had a frustrating start, completing just six laps before being forced into the pits with a gearbox issue and ending the morning with the 12th-fastest time.
The drivers had trouble gripping the smooth Noida surface, with Williams driver Pastor Maldonado and McLaren's Sergio Perez both spinning out onto the grass at turn six before returning to the track without serious damage to their cars.
Hamilton found himself briefly in the gravel after failing to take turn one on his 12th lap of the session, while Marussia's Jules Bianchi and Paul Di Resta also spun off.
Tire supplier Pirelli has dropped the more durable hard compound tires for the Indian surface, instead opting for soft and medium options.