Lee (2-0) allowed only one run over nine innings, walking none and striking out 11 to give the Rangers the first post-season series win in their franchise history.
The left-hander, obtained by the Rangers from Seattle in a trade deadline deal, notched his second win in the series. He threw 120 pitches, 89 of them for strikes.
Nelson Cruz came in to score on catcher Kelley Shoppach's fourth-inning throwing error, one of two miscues committed by the Rays, and Ian Kinsler smacked a two-run homer in the ninth inning for the victors.
Texas advances to its first-ever AL Championship Series, hosting the New York Yankees starting Friday.
Rays starter David Price (0-2) yielded three runs on eight hits over six frames.
Jason Bartlett went 3-for-4 and Ben Zobrist drove in the only run for AL East champion Tampa Bay, which failed in its bid to make the ALCS for the second time in three years.
Copyright 2010 United Press International, Inc. (UPI).