The result means the battle for the title goes down to the final race in Brazil this weekend, with Vettel, champion for the last two years, holding a 13-point lead over Alonso, who was world champion in 2005 and 2006.
Victory for Alonso at Interlagos would give him his third drivers' crown if Vettel finishes lower than fourth.
Second place for the Spaniard would mean he would only win the title if Vettel failed to make the top seven. Third spot for Alonso would require Vettel to finish lower than ninth.
Vettel would become only the third driver to win three titles in a row if he secures victory in Brazil, following Juan Manuel Fangio and Michael Schumacher.
The German has suffered two of Red Bull's alternator failures, one when he was dominating the
European Grand Prix in Valencia
and another when running sixth in the Italian Grand Prix.
The part is supplied by Red Bull's engine partner Renault.
Alonso wants 'special race' in Brazil
Red Bull were running an older version of the alternator, of similar configuration to the one that failed in Vettel's car, whereas other Renault-engined teams have switched to a modified version.
Team boss Christian Horner said: "It's just a worry, full stop.
"Unfortunately it is the third alternator we've had and there have been others in other cars. The new version has raced on other engine cycles and hopefully that's what we'll have for Brazil."
Red Bull's chief technical officer Adrian Newey said: "The component is not a new component. It has been on the Renault engine since about 2005 and it has been failing since 2005 as well."
Although Vettel has suffered more alternator failures than Webber this year, the Australian has borne the brunt of the team's reliability problems.
Alonso and Ferrari are hoping that these will help them overturn the deficit and lead to the Spaniard being crowned champion
Alonso must finish on the podium to stand a chance of snatching the title from Vettel
Victory for Alonso would give him the title if Vettel finishes lower than fourth
Second place for the Spaniard would mean he would only win the title if Vettel failed to make the top seven
Third spot for Alonso would require Vettel to finish lower than ninth
Alonso, who fought up from a seventh-place start to finish third in Austin, said: "Obviously we had a tough weekend; so many difficulties. We were not competitive, we did not have the pace, and Red Bull were very quick and everything was smooth for them.
"Finishing on Sunday afternoon losing only three points was like a victory for us but we need to think of Brazil [and] take all the opportunities we can have there.
"Today we saw Webber's retirement: sometimes it is the water, sometimes the Kers, sometimes the alternator but always in that car, so maybe one day it happens in the other car and we need to be ready."
Ferrari team boss Stefano Domenicali added: "We have seen today Mark had a reliability issue and that can happen every time.
"But I want to stay concentrated on the job we have to do - prepare the car to the best [standard] we can.
"We always said that we need to improve our qualifying pace. Unfortunately here we needed a better position. We had one of the worst qualifyings in our championship so we need to be in Brazil in a different situation otherwise it will be very difficult."
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