Gerrans edged out Slovakia's Peter Sagan, last year's green jersey winner, in a photo finish with Spain's Jose Joaquin Rojas in third.
Belgium's Jan Bakelants, winner of the second stage, holds on to the overall race leader's yellow jersey by a one-second margin while Sagan's second place allows him to take the green jersey for the best sprinter from Marcel Kittel.
The German Kittel had won the opening stage of the race in Bastia on Saturday.
“The team did a fantastic job in looking after me today,” Gerrans told Eurosport after the win. “This is a stage I pin-pointed a little while ago and luckily I had the legs to win a first Tour stage for Orica-GreenEdge.
“I managed to hold off one of the quickest guys around so I’m wrapped,” he said. “It was so close and neither of us knew who won when we finished.”
Gerrans' sprint success came at the end of a stage that was short but tricky, with the route up Corsica's west coast featuring practically no flat sections and a total of four climbs, most notably the testing category two ascent of the Col de Marsolino just 13.5 kilometres from the finish in Calvi.
That climb saw the peloton catch a breakaway of five riders, led by Dutchman Lieuwe Westra and Simon Clarke, a teammate and compatriot of Gerrans.
It was a good day all round for the team, with Simon Clarke featuring in a group of five riders who broke away from the peloton early and going on to reach the summit in each of the first three categorised climbs of the day.
It was a short but tricky stage, with the route up Corsica's west coast featuring practically no flat sections and a total of four climbs, most notably the testing category two ascent of the Col de Marsolino just 13.5 kilometres from the finish in Calvi.
That climb saw the peloton catch the five-man breakaway, which had been led by Dutchman Lieuwe Westra.
Apart from the break, it was a largely uneventful ride for the most part, albeit amid some absolutely spectacular scenery.
The Corsican section of the 100th Tour is now over, and the riders were due to depart for the French mainland later on Monday ahead of a short team time-trial in Nice on Tuesday.
Earlier in the day Britain's Team Sky rider Geraint Thomas started the third stage despite suffering from a fractured pelvis.
The 27-year-old Welshman underwent tests in Bastia on Saturday after falling in a mass crash towards the end of the first stage, and the official Tour medical report after the second stage confirmed that he was receiving treatment for a sore left hip.
French television reports on Monday indicated that new tests revealed the fracture, and Thomas was visibly struggling during the short but tricky 145-kilometre ride up Corsica's west coast from Ajaccio to Calvi.
The two-time Olympic team pursuit gold medallist was seen receiving treatment from the Sky medical team at the back of the peloton and his condition will be of great concern ahead of Tuesday's team time-trial in Nice.
Elsewhere on Monday, the Tour's 198-man field was reduced by two, with Kazakh rider Andrey Kashechkin of the Astana team the first to abandon the 2013 race, at the start of the third stage.
Soon after, Frenchman Yoann Bagot of Cofidis became the second rider to withdraw.