Lee (5-2) fanned five while throwing 85 of his 115 pitches for strikes.
He had not had a complete game or a shutout since producing six of each during the 2011 season. He posted a 17-8 record with the Phillies that year, but went 6-9 last season despite putting together a 3.16 earned run average.
Lee also had two hits on Wednesday and boosted his batting average in 2013 to .316. It was the 12th shutout and 27th complete game of his 12-year career.
Delmon Young put Philadelphia in front with a solo homer in the fourth, his second in as many games. Dominic Brown tripled home a run in the sixth and then scored on a single by Freddy Galvis.
Kevin Slowey (1-5) suffered the loss, surrendering a run on six hits in five innings.
Philadelphia won twice in the three-game series.