The Bahrain Victorious rider, who had come second over the previous two stages, sprinted to victory on the uphill finish in Saint-Haon-Le-Vieux on Tuesday.
The 31-year-old Italian had clinched second place in the previous two stages, closing the gap to within two seconds of Pöstlberger in the general classification.
"After two second places, I really wanted to take a beautiful win. I can thank my team, they worked perfectly. The final kilometre was very hard. (Michał) Kwiatkowski pulled really hard until the last 300 metres. Then (Alex) Aranburu went very strong, I followed his wheel and it worked well for me," said Colbrelli.
Alex Aranburu finished second, with Brandon McNulty coming from behind to snatch a podium place.
Bahrain Victorious rider Jack Haig and Richie Porte of Ineos were the best placed Aussies on stage three finishing in 24th and 25th place.
Belgian Loic Vliegen, who starred in the day's breakaway alongside Israeli Omer Goldstein, built a sizeable lead before he was caught by the peloton before the last twenty kilometres.
Britain's Geraint Thomas, the favourite in the lead up to the event is well placed in eighth in the general classification, 24 seconds off the lead.
Porte, Haig and fellow Australian Ben O'Connor of AG2r are also 24 seconds behind of the overall race lead.
The fourth stage between Firminy and Roche-la-Molière is the only time-trial of this year's Dauphine with the mountainous 16.4-kilometre route set to challenge the race's top riders.