The Tampa Bay starter permitted only three hits at Yankee Stadium on Friday night. Too bad for him, all of them left the ballpark.
"Overall, I thought I had really good stuff," Odorizzi said.
"The first two were good pitches. The McCann one was down and away and off the plate, and the A-Rod one was a first-pitch slider away and he was out in front of it and just yanked it," he said. "The last one was a bad split that just stayed middle and didn't drop, so that was the most frustrating one."
McCann tied a career high with his 24th home run in the fourth. The solo shot made him 11 for 17 with seven extra-base hits against Odorizzi (6-8), including three home runs.
As for his struggles against McCann, "I'm just not going to talk about it anymore, so no further questions on that," the pitcher said.
Evan Longoria hit his third homer in two games for the Rays, still on the edge of the wild-card race despite seven losses in 11 games.
Tampa Bay outhit the Yankees 9-4.
"Little bit of a strange pitching duel. We got the hits but couldn't get anything across and (Odorizzi) didn't give up anything. The ones he did left the ballpark," Rays manager Kevin Cash said.
Sizzling rookie Luis Severino won his third straight start and Rodriguez hit his 681st career home run. The Yankees hold the top AL wild-card spot and are a half-game behind East-leading Toronto.
The 40-year-old Rodriguez gave the Yankees the lead with a two-run drive in the second inning and the 21-year-old Severino kept them ahead.
Severino (3-2) hit 97 mph with his fastball and threw shutout ball until Longoria's homer in the sixth. The righty has a 2.04 ERA after his first six big league starts.
Severino worked around seven hits and three walks in 6 1-3 innings, striking out five. He slapped his hand into his glove after fanning Kevin Kiermaier with high heat to end the sixth with two runners on, protecting a 3-1 lead.
Odorizzi went 6 2-3 innings and fell to 0-3 against the Yankees this season. He is winless in his last seven starts overall. In 10 starts this year, he's gotten either one run or none while in the game.
McCann drew a leadoff walk in the second and Rodriguez followed with his 27th homer of the season and first since Aug. 20.
Bird connected on a two-run drive in the seventh, the fourth homer for the rookie first baseman. He again filled in for Mark Teixeira, the team leader in home runs who was put on the disabled list before the game with a bone bruise on his right shin.
Rays: OF Steven Souza took batting practice on the field before the game, and will start a rehab assignment Saturday with Triple-A Durham. He's been out a month since a pitch from Boston's Joe Kelly broke his left hand. He's hit 15 homers in 89 games for the Rays this year. He could rejoin the team next week in Detroit.
Yankees: CF Jacoby Ellsbury left after four innings because of an upset stomach.
Rays: LHP Matt Moore (1-3, 8.78) returns to the majors after going 2-1 during a tuneup trip to Triple-A, including a 16-strikeout performance. He came back from Tommy John surgery on July 2, made six starts for the Rays and was sent down.
Yankees: RHP Nathan Eovaldi (14-2, 4.17) is 9-0 in his last 13 starts, the longest winning streak in the majors this season.
Logan Forsythe singled in the Tampa Bay second, tying a team record set by B.J. Upton in 2011 of reaching base in nine straight plate appearances. He struck out in his next at-bat. Forsythe is 10 for 14 with four doubles and a triple in his last four games.