Lee's 31st RBI of the season gave Houston a 5-0 lead, but Texas came within 5-4 in the bottom of the eighth on Frank Catalanotto's run-scoring double.
Miguel Tejada had two runs, three hits and one RBI. Mark Loretta, Ty Wigginton and J.R. Towles added one RBI apiece and three players had two hits each for the Astros, who have won three of five.
Winner Brandon Backe (3-5) was charged with three earned runs and five hits in 6 1/3 innings with no walks and five strikeouts.
Closer Jose Valverde threw the final 1 1/3 innings to record his 12th save, striking out the side in the ninth.
Milton Bradley hit a two-run homer and David Murphy added a solo shot in the seventh for the Rangers, who tried for a three-game sweep.
The losing pitcher was starter Kason Gabbard (1-1).