The Aprilia rider, who started on the front row in second place, beat reigning world champion Bagnaia by 1.989 seconds.
The win will have helped erase the memory of Espargaro's premature celebration at last year's Catalunya GP, when he was one lap away from sealing second position but thought the race was over and began waving to his fans.
"I'm so happy, it's my first sprint victory and it's on home soil, so great. Now I'm focused for tomorrow," said Espargaro, who was born in Granollers, seven kilometres from the Circuit de Barcelona-Catalunya.
Pole-sitter Bagnaia, who earlier set a new lap record in qualifying, was harried by Espargaro throughout the first half of the race before the latter found the breakthrough with six laps to go.
As Espargaro began to coast away from Bagnaia in the final few laps, the Italian had to hold off a late challenge for second place from Aprilia's Maverick Vinales - who finished third.
"I expected a little bit more. I don't know why the front tyre dropped so much and I could not make the attack when it was time," Vinales said. "I'm very happy for the team, the entire weekend has been fantastic so far."
Despite not winning, Bagnaia moved a further four points clear of Jorge Martin (Pramac Racing) in the overall standings, taking his lead up to 66 points. Marco Bezzecchi (VR46 Ducati) is nine points behind Martin in third.
"Obviously it's better to win, but I'm happy with the result. The result is positive, we gained points for the championship and that's the main thing for sure," Bagnaia said.
Rain threatened to wreak havoc early on but despite the dark clouds, the weather remained manageable throughout and riders just had to contend with drizzle on a few sections of the track.
Yamaha's Fabio Quartararo, the 2021 world champion, finished 18th while six-time MotoGP champion Marc Marquez ended in 11th. Espargaro's brother Pol was unable to finish the sprint after crashing out early.
