Bagnaia on his factory Ducati reeled in race leader Martin before the Italian passed him on lap 20 at turn five where he crashed out of the sprint on Saturday, to claim his third victory of the season.
Martin could not respond and Bagnaia triumphed by nearly two seconds to cut the gap on the Spaniard to 39 points in the standings.
Home favourite Marc Marquez came in third ahead of Aleix Espargaro, who announced he is retiring at the end of the season earlier this week.
Marquez is third in the standings, 41 points behind compatriot Martin.
"Honestly I was very angry about yesterday (his crash in the sprint whilst leading on the last lap) but I knew the potential I had and was able to win the race," said Bagnaia.
"(It was a) tough start but then I saw some struggling at the front and I pushed more.
"The bike was amazing, the team did an amazing job setting up the bike and now I'm looking forward to the next race (next weekend's Italian MotoGP)."
Seventh at lights out on his Pramac Ducati, Martin got through on Pedro Acosta for second and then Bagnaia on turn 10 to take the lead with 20 laps to go.
Youngster Acosta was in hot pursuit on the day after his 20th birthday but skidded off the track in lap 11, rejoining in 20th place.
After Bagnaia passed Martin towards the end he kept the overall leader at arm's length to clinch victory.
"I am super happy, super proud, starting from seventh I executed perfectly the first corner and into fourth," said Martin.
"Towards the end I tried to keep the pace but had nothing left in my pocket.
"I tried to put some pressure on Bagnaia but there was nothing left and it was complicated."
After a sluggish start Marquez, aiming for a first MotoGP win since 2021, charged forward from 14th spot on the grid on his Ducati-Gresini.
He finally got past Aprilia rider Espargaro to claim a podium spot.
Espargaro, 34, won the sprint on Saturday and was hoping to do the double at Catalunya as he did last year, but was left frustrated despite starting on pole.
"I had a bad start, however, step by step I made up ground -- I was patient as I knew the race was long," said Marquez, who was recording his third successive podium finish.
"I was able to defend third, I was sorry for Aleix as it was his final race in Catalunya but delighted to be back among the top guys again."
