Lee, 6-0 with a major league-leading 0.81 ERA, started the second game for the Indians, but left after nine innings of scoreless ball. The Blue Jays would win with three runs in the 10th inning.
Carmona (4-1) struck out three and walked four in his second shutout and third complete game in 47 big league starts.
"We know our starting pitching is extremely strong," said David Dellucci, whose two-out single in the sixth drove in the first run. "The way Fausto was pitching, we knew it wouldn't take a lot."
A.J. Burnett (3-4) gave up three runs and five hits in 7 2/3 innings for the Blue Jays, who have been blanked in 22 consecutive innings.
Cleveland won for the fifth time in six games and extended the Blue Jays' losing streak to four. The Indians outscored Toronto 21-1 in the first three games of the series, and the Blue Jays have lost nine consecutive games in Cleveland.
Burnett allowed only one hit until Grady Sizemore doubled off the wall in right-center with one out in the sixth. Sizemore went to third on a groundout by Jamey Carroll and scored on Dellucci's single.
"That's a big two-out knock in a zero-zero ballgame," Cleveland manager Eric Wedge said.
Cleveland's defense helped Carmona. With Scott Rolen on first and one out in the fourth, Matt Stairs lined a single to right and Ben Francisco made a one-hop throw to third baseman Casey Blake to retire Rolen.
- Burnett dropped to 30-34 with a 4.31 ERA when starting with more than four days' rest. He's 42-36 with a 3.43 ERA when starting on normal rest.
- Stairs had three of Toronto's hits.
- Carmona fanned Aaron Hill three times -- Carmona's only strikeouts.
- Burnett is 1-4 in five starts against the Indians, including 0-4 in Cleveland.
- Indians OF Shin-Soo Choo, recovering from elbow surgery last September, is expected to begin a rehab assignment this week at Triple-A Buffalo.