That was also Boston's last hit with a runner in scoring position. The Red Sox were 0-for-11 in those situations for the remainder of the game.
A big reason for that was Ortiz being walked every other time he came to bat with runners in scoring position; he was walked intentionally in the eighth, 10th and 12th innings.
"It's not frustrating. ... It's not like now or never," said Ortiz, who was 2-for-2 with a double and four walks. "Situations come, I've just got to be patient. I don't mind taking walks -- been part of my game for
years. ... You've got to take what they give you."
Rodriguez's hit in the 13th inning scored Gary Sheffield from second base. Jonathan Papelbon (0-2) hit Sheffield with the first pitch of the inning, and Sheffield stole second with one out and Carlos Guillen at the plate.
"I knew we needed a run, so I waited for a high leg kick and went," said Sheffield.
And with two outs, Rodriguez hit his liner to right-center that just eluded Crisp.
"You can't try to do too much against him," Rodriguez said of Papelbon, who hadn't allowed an earned run on the road this season. "All I did was relax at the plate and throw my bat at the ball."
Jason Grilli (3-2) got the win for the Tigers. Though neither was involved in the decision, both Boston starter Kason Gabbard and Detroit's Jeremy Bonderman were outstanding.
Gabbard allowed two runs and only three hits over 6 1/3 innings, walking two and striking out three.
"I felt a lot better than I did my last two starts with my fastball," Gabbard said. "That's the key -- throwing my breaking balls off of my fastball."
The southpaw left in the seventh after surrendering a one-out single to Guillen.
The Red Sox jumped out to a 2-0 lead in the first on Ortiz's two-run homer. Dustin Pedroia, who had tripled with one out, scored ahead of Ortiz's 14th long ball of the season.
Boston then threatened to score more when Manny Ramirez followed with a walk and J.D. Drew singled. But Bonderman got out of the inning by striking out Mike Lowell and Jason Varitek.
Bonderman allowed only four hits and a walk over the next seven innings, before giving way to closer Todd Jones, who started the ninth. Bonderman walked three and struck out nine.
Detroit tied it at 2 in the fifth on only its second hit of the game. Gabbard walked Magglio Ordonez and Guillen to start the inning. He then retired Rodriguez on a tap between third base and the mound, on which the runners
moved up to second and third. Marcus Thames then fouled out to first, on which Eric Hinske made a nice play leaning over the tarp down the first-base line. But Craig Monroe
one-hopped the left-field wall with a line drive that went for a double and brought home Ordonez and Guillen.
The Red Sox couldn't capitalize on an opportunity to take the lead in the sixth. Ortiz led off with a double and moved to third on Ramirez's flyout to deep center. But Bonderman struck out Drew looking, and Lowell fouled out to Thames at first.
Another opportunity went by the wayside in the eighth, when Pedroia hit a one-out double. Ortiz was walked intentionally and Ramirez hit a grounder to third baseman
Brandon Inge, who knocked down the ball and was able to force Ortiz at second. Drew struck out swinging to end the inning.
Ramirez hit into a double play in the 10th with runners on first and third to end that inning.
Hideki Okajima worked his way out of a bases-loaded, one-out jam in the 10th, as Omar Infante flied out to center to end the inning.
Monroe fouled out with the bases loaded in the 11th. Red Sox pinch-hitter Kevin Youkilis flied out with the bases loaded in the 12th.
Boston will try to avoid being swept in the three-game weekend series on Sunday afternoon behind Daisuke Matsuzaka.
"It's disappointing, it's a long night," said Red Sox manager Terry Francona. "We need a quick turnaround."