Coulthard was ecstatic to claim his first official V8 Supercars Championship win.
"We got three fake ones at the Australian Grand Prix and it's great to get one under the belt,'' the New Zealander said.
"We came in confident after the performance at the Grand Prix. You can't ask for much more and the team did such a great job today.''
It was not all plain sailing for Coulthard, who had to fight off Winterbottom over the closing laps of the first super-sprint race to give him the critical front row of the grid for the second race, which began with a rolling start.
Following his impressive move under Whincup, Coulthard opened up a solid lead only to be forced to do it again after a safety car with five laps remaining. Some light rain fell over the last three laps to add to the anxiety before he could celebrate victory.
The only impediment to glory may come with a post-race investigation into his restart when he looked to get a flyer, although it did not stop the Kiwi standing on top of the podium to receive the winner's trophy for the first time in 180 starts since joining the championship in 2004.
"The restart looked okay to me,'' said team boss Brad Jones. ``It's his first time ever leading a race and in this position and he seemed to maintain his pace to me. I certainly didn't see anything amiss. It was a great result for the team.''
It proved another tremendous day for New Zealand drivers with Shane van Gisbergen finishing seventh, rookie Scott McLaughlin eighth and Jonny Reid in 24th.
McLaughlin moves to fifth overall in the championship with van Gisbergen eighth and Coulthard 16th after three races.
There is a further race today with the same format before the V8 Supercars troupe head across the Tasman to the revamped Pukekohe Park Raceway, which is a similar track to yesterday's race at Symmons Plains.