Ortiz tagged and went to third on Daniel Nava's fly ball, then was nearly caught too far off the bag when Jarrod Saltalamacchia struck out and catcher Jose Molina threw to third base trying to pick off Ortiz. The inning ended with Stephen Drew hitting a grounder back to Cobb.
The Rays wasted opportunities against Buchholz, too.
James Loney doubled off the left-field wall to begin the second inning, but was erased when Desmond Jennings lined into a double play.
The Rays loaded the bases on two walks and Loney's second hit of the night, but Buchholz escaped the jam by fanning Matt Joyce.
Buchholz wasn't as fortunate in the fifth, when Yunel Escobar beat out an infield single and David DeJesus doubled with one out. Zobrist popped to shortstop, bringing up Longoria, who became the second player in major league history to hit a postseason homer on his birthday.
Willie Mays Aikens homered twice for Kansas City on his birthday Oct. 14, 1980, against Philadelphia in Game 1 of the World Series.
Longoria's home run was his ninth in 109 career postseason at-bats.
Loney had three hits off Buchholz, who allowed three runs, seven hits and struck out five in six innings.
Ellsbury scored Boston's first two runs, on Zobrist's throwing error in the first and Cobb's wild pitch in the fifth. Ortiz's fifth-inning RBI single put the Red Sox up 3-0 against the Tampa Bay starter.
NOTES: Rays rookie Wil Myers left before the eighth inning because of cramping in both legs. A leading contender for AL Rookie of the Year, Myers took an awkward swing on a foul ball in the seventh and grabbed the area around his left calf. He limped back to the dugout after striking out for the third out. Myers went to right field after the inning, then headed back to the infield and was met by a team trainer. The club said he received IV fluids, and Maddon said Myers probably will be fine for Tuesday night's game. Joyce, the DH, replaced Myers in right field.
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