"It is a credit to all the guys behind me," the 25-year-old said. "After yesterday blowing two right rears yesterday they turned this car upside down. The whole win is on those guys.
"It means a lot - to be leading in Tassie to be leading and make a mistake - to win the next weekend is big."
The podium for Winterbottom also breaks a run of poor results for the 2015 champion.
"It is all about surviving," he said. "It is crazy racing like that. They made rule changes and [we had] car changes and you just are counting the laps down."
It was a tough weekend for the three Kiwis in the field. Scott McLaughlin was the best of them, finishing 14th despite looking like he had the fastest car. He was caught out with strategy and couldn't recover late in the race.
Red Bull Holden Racing was one of the only teams to avoid tyre dramas on Saturday but within the space of a lap both Shane van Gisbergen and Jamie Whincup had right rear tyres explode. The Kiwi finished 16th with Whincup in 18th.
Late in the race the third car in the stable, driven by Craig Lowndes, had his right front blow as well.
Championship leader Fabian Coulthard also had problems. The Shell V-Power Racing driver was handed a drive-through penalty for failing to stop at a red light when re-entering the track during a safety car intervention. He had to settle for 17th.
"We thought we were pretty good on tyres so we went in today pretty confident," van Gisbergen said. "No issues yesterday and the cars were pretty much the same so it was a big shame.
"It sucks.
"It was average racing going like that going into every corner wondering when the tyre was going to pop."
It means Coulthard holds a seven point lead in the championship from van Gisbergen with Mostert 30 points back in third.
Championship Standings
Fabian Coulthard 568 points
Shane van Gisbergen -7
Chaz Mostert -37
Jamie Whincup -46
Scott McLaughlin -97
