Di Giannantonio, who does not have a MotoGP seat next season, threw caution to the wind at the floodlit Lusail International Circuit and took on Bagnaia to claim his first win while pole-sitter Luca Marini of VR46 Racing finished third.
Victory marked a special weekend for Di Giannantonio, who also finished second in Saturday's sprint.
"Man, what do I say. It's been an incredible weekend the race was unbelievable. I was struggling with the front (tyre) but I saw Pecco (Bagnaia) making little mistakes," a grinning Di Giannantonio said in a post-race interview.
"This was revenge, first for myself and others with me. Now we did it, now I'm a MotoGP winner."
Bagnaia lost the lead with four laps to go but the Ducati rider has still put one hand on the rider's championship after extending his lead over Martin to 21 points.
The Italian can even secure back-to-back world titles in Saturday's sprint at the season-ending Valencia Grand Prix next weekend.
Bagnaia and Martin started fourth and fifth on the grid - separated by seven points - but it was the Ducati rider who had the perfect launch as he shot off the line to take the lead from Marini going into turn one.
Wheel spin
On the other hand, Martin nearly lost control of his Pramac bike due to wheel spin, dropping to eighth in the opening lap, and he was forced to pick his way through the pack as Bagnaia surged ahead.
While Bagnaia kept Di Giannantonio at arm's length, Martin was falling further behind and he lost so much pace that even the slower Honda of Marc Marquez, Yamaha's Fabio Quartararo and KTM's Jack Miller managed to get past the Pramac rider.
Up front, Di Giannantonio did not let up. With four laps to go, he ignored team warnings and made his move to get past Bagnaia.
The Ducati rider nearly threw it away on the next lap with a risky move to retake the lead at turn one where he ran wide and then backed off while shaking his head, knowing second place was better than nothing.
"We managed to do a perfect start, I tried to create a gap but Diggia (Di Giannantonio) was incredible. I got sucked into his slipstream at the first braking (zone) and I went wide," Bagnaia said.
"But we've managed to open a gap on Jorge."
Once Bagnaia saw Martin had finished 10th, there were no hard feelings as he and several other riders stopped their bikes by the side of the track to congratulate an emotional Di Giannantonio.
