Stoner fined for track rage during French MotoGP
But he also left with a 5000 euros ($A6,687) fine after striking French rider Randy de Puniet on the arm during the morning warm-up session.
The Honda star lashed out at de Puniet on track after the Pramac Ducati rider moved into his path while going significantly slower.
Stoner didn't let the incident affect his race.
He was jumped by Spain's Dani Pedrosa at the start but regained top spot on the second lap and rode to victory by more than 14 seconds from Andrea Dovizioso with Valentino Rossi third.
Pedrosa crashed out when battling for second, breaking his collarbone in the process.
The victory saw Stoner climb within 12 points of Jorge Lorenzo in second position on the championship standings.
Stoner said later he and de Puniet had settled their differences following their clash.
"I went and spoke to Randy, and he apologized immediately,'' he said. "I then of course felt bad, so I apologized. We spoke a little bit and we have no problems. And that was as far as it went. But we still got penalized for it.''
After winning the season opener in Qatar, Stoner had fallen back following a much-publicized crash with Rossi in Spain and a third-place finish in Portugal.
And the Australian was delighted to be back in the hunt.
"It's been an awesome weekend and from start to finish everything has been amazing,'' said Stoner. "I'm just really looking forward to the next race now. It was good to get some points back today.''