Lowe (4-1) won for the fourth time in five starts this season, handcuffing the Angels on three hits while walking two and striking out one.
The right-hander tossed 62 of his 107 pitches for strikes and lowered his ERA to 2.27 with the victory, which gave the Indians the rubber match of a three-game series against the Angels.
Cleveland scored two runs in the fifth when Torii Hunter lost Asdrubal Cabrera's routine fly ball in the sun and added another in the eighth on pitcher Kevin Jepsen's errant throw to first on a Jack Hannahan bunt.
Carlos Santana finished 3-for-4 with a run scored for the Tribe.
Angels starter Ervin Santana (0-5) was saddled with the loss after yielding two unearned runs on seven hits in a seven-inning effort.
Los Angeles fell for the sixth time in seven games.