The Astros ended a four-game losing streak, getting a nine-strikeout performance over seven innings from Bud Norris.
Houston built a 7-1 lead through three innings, with Lee's two-run single highlighting a three-run third. Lee also scored during Houston's two-run first on a double by Jed Lowrie.
Norris (4-1) allowed one run on four hits to get the victory. Milwaukee's final two runs came in the ninth off Rhiner Cruz before Wesley Wright came on to get the final three outs in a non-save situation.
Randy Wolf (2-4) was charged with the loss after giving up seven runs on seven hits in four innings.