The 21-year-old German grabbed the second pole position of his career, and the first for his Renault-powered team, with a last-gasp lap of one minute 36.184 seconds
With his Red Bull team mate Mark Webber [ Images ] third behind Alonso, the previously dominant Brawn GP cars of Rubens Barrichello [ Images ] and Jenson Button [ Images ] were pegged back in fourth and fifth.
"Unbelievable that we made it to pole," said Vettel, who became Formula One's youngest race winner in Italy [ Images ] last year with Toro Rosso. "It was not easy. We had some problems with the car and we tried to run as little laps as possible."
Spaniard Alonso, who clocked 1.36.381, was an equally surprising presence in second for Renault, who made some radical changes to their car as they scrambled to catch up with the teams using the controversial rear diffusers.
"It has been strange for us with a completely new car, we went in to qualifying with some doubts and we are very happy with the result for sure," said the twice former world champion.
Australian Webber's time of 1.36.466 was enough to beat the Brawn of Barrichello in fourth with the Brazilian's British team mate Button, who won the first two races of the season from pole, in fifth.
"We knew they were competitive but we didn't think they were quite that competitive," championship leader Button said of the Red Bull duo.
"It's a pity that we are starting behind them because its very tough here to overtake. So we'll see what happens."
Toyota's [ Images ] Jarno Trulli [ Images ] and Nico Rosberg [ Images ] of Williams, both using the diffuser that was declared legal at an appeal hearing earlier in the week, were sixth and seventh ahead of the last two world champions, Kimi Raikkonen [ Images ] of Ferrari [ Images ] and Lewis Hamilton [ Images ] in the McLaren [ Images ].
Although Ferrari continue to struggle with Felipe Massa [ Images ] missing out on the last round of qualifying and languishing in 13th place, defending champion Hamilton saw promise in his ninth place.
"Bit by bit we're catching these guys," said the 24-year-old, who took part in the third section (Q3) of qualifying for the first time this season.
"But there's a very long way to go so we've just got to keep on churning away."
Trulli's team mate Timo Glock [ Images ] missed out on the top 10, having had his gearbox replaced, and the German will be relegated from 14th to 19th on the grid for Sunday's race.
BMW-Sauber had a very disappointing day with Poland's Robert Kubica [ Images ] dropping out after the first session and Nick Heidfeld [ Images ], second in Malaysia, pipped to a place in Q3. They will start 18th and 11th respectively.
"Data evaluation from free practice indicated our car would not work on this track," said team boss Mario Theissen.