The Australian's win means the series has had seven different winners from seven races so far this season.
Power made a better start than pole-sitter Robert Kubica and edged ahead of him into the Dunlop Curve. He pulled out enough of a lead to remain at the head of the field once the mandatory pitstops had been completed. Championship leader Kubica reeled in Power at two-thirds distance, but settled for second after being unable to make a move on the Carlin Motorsport driver.
It was Power's first victory in any discapline since he won the Champ Car-supporting Formula Three race at Surfers Paradise in 2002. He said: "I made a good start and chose not to leave my pitstop too late. Kubica got close at one point but I held him off. I have been fast all season I knew I would win at some point - this could be a turning point in my career."
Colin Fleming made the most of his pit strategy to finish third. The American, who had started sixth, was one of the longest to stay out on the track. When he emerged form the pits, he had vaulted Cram Competition's Eric Salignon and Draco's Markus Winkelhock. It was the Red Bull-backed driver's first podium of the year.
Salignon finished fourth, ahead of race-one winner Winkelhock.
The 2015 Formula Renault 3.5 season will be notable for being the last with the French company's backing but also produced a worthy champion in Oliver Rowland. PETER MILLS evaluates this year's crop of drivers
Last year's field was extraordinary and hard to match, but the Formula Renault 3.5 grid will still have plenty of talent this season. Glenn Freeman runs through the field ahead of this weekend's season opener
Landing the Fortec seat that took rising star Robin Frijns to the 2012 FR3.5 title was already a good sign for Stoffel Vandoorne. Then McLaren took him under its wing. Peter Mills tells Vandoorne's story so far