The German took the lead on the first lap when front-row starters Felix Porteiro and Patrick Pilet collided at Roggia, and both took a trip through the gravel.
Winkelhock and second-placed Adrian Valles made their mandatory pitstop together but the German's Draco Multiracing USA team took only 5.612 seconds to change all four tyres and he led the Spaniard out of the pits.
Winkelhock then pulled away and won by more than six seconds. However, the result wasn't enough to take the second place in the Championship away from Valles.
"We made some changes after qualifying and they worked. It was still a brilliant way to end the season," Winkehock said.
Ryan Sharp finished third on the track but was immediately docked 20 seconds after the chequered flag by race stewards, because he did not make his mandatory pitstop during the specified window.
Sharp had pulled off into the pitlane after the formation lap and changed his tyres before the race started. Mandatory pitstops must be made between laps five and 18, and the former GP2 racer continued to stay out on track after lap 18 on the same set of tyres, to the amazement of the onlookers.
Winkelhock and Valles both passed Sharp in the latter stages and neither realised it was a fight for position. Sharp was classified seventh with the 20-second penalty, which is less time than a pitstop at the Italian circuit.
Pilet managed what he couldn't in the first race by successfully passing Felix Porteiro in the latter stages. He finished third scoring and his first podium of the season.
Pilet's result was impressive considering he was dropped by Jenzer Motorsport mid-season for Sharp. After months on the sidelines he was rescued by GD Racing and given a drive for the last two rounds of the series.
"I have to thank Jenzer Motorsport for dropping me," Pilet quipped. "Now I am with a good team."
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