McLaren's Jenson Button
drove a composed race to take second place, ahead of a spirited Nick Heidfeld who capitalised on a brilliant start to round off the podium places in his Renault.
"Fantastic job. In the heat we kept our heads cool. Thank you," Vettel told his Red Bull team over the radio after winning his fourth race in a row.
"A pleasure every weekend to be with you. I'm loving it."
Vettel's team mate Mark Webber did well to claim fourth place following a poor start as both Red Bulls ditched the KERS boost system mid-race after suffering reliability issues.
On an afternoon when nursing the tyres through each stint was key and the threat of rain always an issue, Vettel drove a faultless race from the front and navigated the flurry of pit stops with a minimum of fuss.
"I think he was the coolest guy here today -- his composure in the car, the way he controlled the race, looked after the tyres, did what he needed to when he had to," Red Bull team principal Christian Horner told reporters.
The Ferraris of Felipe Massa and Fernando Alonso took the next two places, with Lewis Hamilton finishing seventh on the track in the other McLaren after he and Alonso collided when they were fighting for third late on.
Two hours after the race, stewards imposed retroactive 20-second time penalties on the former world champions for driving infringements, dropping Hamilton to eighth place behind Japanese Sauber driver Kamui Kobayashi.
Alonso's position remained unchanged with Mercedes's Michael Schumacher and Force India's Paul di Resta making up the final two points scorers.
The Renaults enjoyed the best of the start, Heidfeld and Russian Vitaly Petrov storming down the outside to get past the Ferraris and Webber and threaten the McLarens and Red Bulls at the head of the field.
Heidfeld reached second place by turn one and held off Hamilton until the first change of tyres, when a poor stop dropped him down the order until he battled back late in the race to match Petrov's third-place finish in Melbourne.
Once Hamilton was clear of Heidfeld, the Briton began to eat into Vettel's lead, but two tardy stops saw him lose track position to Button, who despite having a faster car than his team mate, was never able to threaten the leader.
"It was a really confusing race in a way, understanding or trying to understand the pit stops and whether it is worth looking after the tyres or not, so pretty tricky," Button said.
"In the last stint, putting the prime tyre on, the car came alive, I had so much more grip."
Webber had a woeful start and was shuffled down the pack to 10th place as he struggled with the KERS system Red Bull had opted against using in the season-opener in Australia.
Running a four-stop strategy, his best stint was the run to the chequered flag when he closed in on Heidfeld in the final three laps after both had leapfrogged Alonso and Hamilton when they were forced to pit late on.
"It's tough to clear people when they have a better KERS," Webber said. "Anyway, it was an interesting grand prix and we keep learning. It's not our day yet but I'm pushing for it to come."
Double world champion Alonso's Ferrari improved as the race progressed and he was battling Hamilton for track position on the 45th lap when he damaged his wing after slamming into the back of the McLaren.
The Spaniard pitted immediately, while Hamilton opted to change the tyres of his damaged car and Heidfeld and Webber overtook him with four laps remaining.
"Obviously I was close, the rear wing didn't work for me in the last part of the race, so I couldn't overtake him (Hamilton) on the straight line which was the best possibility," Alonso said.
"Unfortunately we touched each other, I broke the front wing and had to pit again. It cost me maybe the podium today, but we will try again in China."
Vettel moved to 50 points with the victory, 24 ahead of Button with Hamilton and Webber a further four points adrift as the series heads to Shanghai for the Chinese Grand Prix next Sunday.