Evan Longoria had three hits, including a two-run home run, to go with three RBI and three runs scored for the Rays in a game that took 5 hours, 27 minutes to complete. Upton and Cliff Floyd homered and Upton and Carl Crawford each drove in two runs for Tampa Bay.
Rays' starter Scott Kazmir went 4 1/3 innings, allowing five runs on six hits -- three of them homers -- with three walks and two strikeouts. David Price (1-0) pitched 2/3 inning in relief to get the win.
Jason Bay led Boston with three hits -- including a homer and a double -- and four RBI. Dustin Pedroia homered twice and scored four runs for Boston.
The Rays got to Red Sox starter Josh Beckett for eight runs on nine hits -- including three home runs -- in 4 1/3 innings. Beckett walked just one and struck out five.
Boston reliever Mike Timlin (0-1) took the loss after walking three batters in the 11th to load the bases for Upton's game-winning sac fly.
The game featured seven home runs, tying a post-season record.