The start of the session was initially delayed by 15 minutes because of visibility problems in the New Delhi smog which forced the grounding of the medical helicopter.
Race control announced a further 15-minute delay moments later, only to then shorten that to five minutes, with the session finally getting underway 20 minutes later than scheduled and the running restricted to 40 minutes.
Vettel, quickest in both of Friday's sessions, needed just one lap on the softer tyres to elevate himself to first place with a time of 1m25.332s. He then focused on longer runs with the soft rubber, which he seemed to struggle on as the blistering issues continued.
The German driver did not even complete a run using the harder compound.
Webber finished second, but over 0.5 seconds behind his team-mate, with Ferrari's Fernando Alonso the first of the non-Red Bull drivers in third, albeit over seven tenths off Vettel.
The decision to shorten the session meant the action was frantic from the start, with most drivers taking to the track right away.
Webber was the initial pacesetter in the Red Bull before Felipe Massa and then team-mate Alonso moved to the top of the times, before the Australian driver regained the top spot moments later.
Twelve minutes in, it was McLaren's Sergio Perez who went quickest by just 0.044s as the top four were covered by less than a tenth of a second.
Alonso then regained first place before Vettel completed his first soft-tyre run with a time that was over 1.5s quicker than anybody else and also the best lap of the weekend so far, a 1m25.332s.
Webber also tried the soft tyres before the halfway point, but the Australian was over half a second off his team-mate's pace.
Red Bull, struggling with the degradation of the soft tyres this weekend, seemed to focus mainly on solutions to extend the life of the rubber.
Despite everyone trying the soft tyres as the session progress, no one could get close to Vettel's time.
The only significant incident of the session involved Hulkenberg hitting one of his Sauber mechanics when returning to the pits. The mechanic took a tumble but got up on his own and seemed to suffer no serious injuries.