Nearly seven hours after Ortiz's ninth-inning homer off Valverde gave the Red Sox a 4-3 victory in the first game of a day-night doubleheader, the Tigers closer retired Ortiz to finish off a 3-0 win in the nightcap.
"It was the same for me -- I didn't feel anything different," Valverde said. "He's a good hitter, and there's nothing you can do about that, but the second game was my time."
In the second game, Justin Verlander (5-3) allowed four hits and walked two in 7 2/3 shutout innings, throwing a career-high 132 pitches.
"He's a real proud guy, and you could see the determination in his eyes," Tigers manager Jim Leyland said. "I checked with him, he said he was fine, and he was up for the challenge."
Leyland said he will take advantage of Thursday's off day to give Verlander an extra day between starts.
"During the -- I don't even know what inning it was, maybe the fifth or sixth -- my velocity started to jump up, and I still didn't feel like I was overthrowing the ball," Verlander said. "I found a rhythm and had my mechanics and the ball was coming out live."
Josh Beckett (4-2) took his first loss since April 5 -- his first start of the season. Beckett gave up two runs on five hits and a season-high five walks in six innings.
"Beckett's stuff was up in the first inning, and he gave up a couple runs," Red Sox manager Terry Francona said. "After that, Verlander never gave us a chance. He's one of the best in baseball. We made him work, but the higher he got into the pitch count, the harder he threw."
The loss ended Boston's five-game winning streak. The Red Sox had won 13 of their last 15 before the night game.
Valverde pitched a perfect ninth for his 12th save, finishing a 10-hour day that included a 50-minute rain delay before the second game.
Ortiz's game-winning homer in the opener was his first pinch-hit home run in eight years.
"I don't like pinch hitting too much, but I did just what I do as a DH," Ortiz said. "I went to the cages, took some swings and got loose."
Ortiz, pinch-hitting for Jarrod Saltalamacchia, worked a full count against Valverde, then hit a line drive over the scoreboard in right-center.
"Valverde is so tough on right-handed hitters, it seemed like a easy decision with David sitting there," Francona said. "He worked the count and got a great swing."
Before Sunday, Ortiz had only faced Valverde once, hitting a grand slam on July 30 of last year.
Boston's Clay Buchholz and Detroit rookie Andy Oliver each pitched six innings and allowed three runs.
Oliver struggled badly in the first inning of his season debut, allowing a double, a walk, a hit batter and four stolen bases, but somehow escaped down just 1-0 on Adrian Gonzalez's sacrifice fly.
"My slide step was a little slow in the first inning," Oliver said of the stolen bases. "From the second inning on, I relaxed and got focused on keeping guys off the bases."
The Red Sox got solo homers from Mike Cameron and Pedroia in the next two innings, but Boston's offense stalled util Ortiz's homer in the ninth.
Andy Dirks homered in the fourth, and Boesch's fourth homer pulled the Tigers with a run in the sixth.
Cabrera followed with a double, took third on Martinez's groundout and scored on Jhonny Peralta's single.
Before the first game, the Red Sox placed reliever Franklin Morales on the 15-day disabled list and recalled right-handed reliever Michael Bowden. ... The second game of the doubleheader was not originally scheduled to be televised, because of ESPN's exclusive Sunday-night contract, but a waiver was reached Sunday afternoon that allowed the game to be shown in both Boston and Detroit. ... Leyland had said he hoped moving slumping Ryan Raburn to second base would give him a "new season." Raburn went 0-4 with three strikeouts, dropping his season batting average to .195, and was out of the lineup for the nightcap.