KTM's Brad Binder finished second, less than a second behind, while VR46 Racing's Luca Marini was third. Ducati's Bagnaia started on the second row but finished seventh.
Martin began the weekend 27 points behind the defending champion and gave himself a boost when he smashed the lap record to secure pole position to make it a perfect Saturday.
Martin had missed out on race victory and the podium at the Australian Grand Prix when he lost grip at the end of the race and the Spaniard said he was trying to conserve his tyres this time.
"But then I saw Brad and Luca (catching up) and decided maybe now it's time to pull away," he said in a post-race interview.
Martin had a flying start to fend off Marini and take the lead going into turn one while Bagnaia, who started sixth, fell to ninth by the end of the first lap.
Binder started fifth on the grid but he managed to make up two places, moving past Aprilia's Aleix Espargaro and VR46 Racing's Marco Bezzecchi to sit third.
Binder has found more success in sprints this season with five previous podiums and the KTM rider eventually overtook Marini to move up to second when the VR46 rider struggled to get the best out of his tyres in hot track conditions.
Martin extended his lead to 1.5 seconds with six laps to go and although Binder was able to catch up, the Spaniard was in complete control as he crossed the line for his seventh sprint win of the season.
"Second place, we'll take it," a smiling Binder said. "In the beginning, I struggled to get past Luca, it was a tricky one. Then Martin did a fantastic job."
Honda's Marc Marquez qualified eighth on the grid and the six-times MotoGP champion, who is moving to Gresini Ducati next season, finished fourth.
