The Rays' right-hander allowed one run on seven hits while striking out six in seven innings to earn his third win of the season.
"Odo was outstanding," Rays manager Kevin Cash said. "He gave us seven really good innings. And it seemed like he probably got a little bit stronger with his fastball command towards the end of the game. So that was good to see."
Odorizzi had just two clean innings. The rest of his outing was dotted with cleanups.
In the first inning, he allowed a one-out double to Dustin Pedroia -- no runs scored. He also allowed a leadoff double to Mookie Betts in the third, a two-out double to Brock Holt in the fourth, and back-to-back singles to David Ortiz and Allen Craig to start the sixth -- no runs scored in any of those innings.
Only when the Red Sox cobbled back-to-back triples by Holt and Xander Bogaerts with two outs in the second did they score against Odorizzi.
Last season, Odorizzi struggled from time to time with damage control, which led to giving up big innings. That wasn't the case Monday night.
The game "probably wouldn't have gone that way last year," Odorizzi said. "But just the experience I gained over that time, the tough times helped me make this into a different time. I felt like there was always somebody on base, and I had to make pitches.
"I know our defense wasn't as sharp as it normally is. It was good to have their back because they've had mine throughout the entire year. So it was good to kind of pick them up when they've had mine."
Odorizzi complimented the Rays' offense for giving him an early 4-0 lead.
"It's good to get the lead," he said. "Especially here. It kind of takes the crowd out of the game. It got a little loud in the fifth or the sixth whenever Ortiz got on on that fly ball. But other than that, they were pretty quiet tonight. But I think that has a lot to do with us scoring first."
Odorizzi entered Monday night's game at 0-2 with an 8.25 ERA in three career starts at Fenway Park.
"It's good to have one here," Odorizzi said. "Last year was a little bit up and down to say the least. But this year is a new year. I'm ready to put that behind me, and I think I went out there and did that today. Just glad to get the team a win. And get deep in the game and save the bullpen a little bit."