Pole sitter Bagnaia eventually finished third while Pramac Racing's Martin, who was second fastest in qualifying, finished a distant fourth to fall 14 points behind Bagnaia in the championship.
The victory was sweet redemption for Bastianini, who broke his shoulder in the season-opening sprint in Portugal while he missed more races after undergoing surgery in September to mend broken bones in his left hand and left ankle.
The Italian was under pressure for results after making the switch to the factory Ducati team and he became the seventh different rider to win a race this season.
"I'm so tired. I gave my 100% today. After a long time without a podium, I've got this victory," an exhausted Bastianini said in a post-race interview.
"My family and friends know what I've had to do to arrive here, it's fantastic."
Bastianini and Saturday's sprint winner Marquez were both quick off the line and left the two title contenders behind on the opening lap with some serious pace up front.
The four riders quickly left the chasing pack behind as Bastianini extended his lead over Marquez while Martin had a couple of looks in as he attempted to overtake Bagnaia.
But as the race wore on, Martin was forced to back off as he looked to conserve his tyres in the searing heat at the Sepang International Circuit while Bagnaia also looked content to bide his time in third place.
"I tried to close the gap to Alex and Bastianini, but I was really struggling with the braking... But I'm happy to keep a gap in the championship," Bagnaia said.
With two laps to go, Martin was nearly six seconds behind Bagnaia and the Spaniard was seen shaking his head, knowing he had missed out on yet another opportunity to close the gap in the battle for the championship.
Yamaha's Fabio Quartararo prevented an all-Ducati top five and spoiled Marco Bezzecchi's 25th birthday when he overtook the VR46 Racing rider in the dying stages to push him down to sixth.
The MotoGP championship has two more races left this season in Qatar and Valencia.
