The AL Central-leading Tigers (54-41) stopped a four-game losing streak and increased their lead over Cleveland to 5 1/2 games.
"It's huge to come and get the win to end that little streak," Smyly said. "But that's baseball, you're going to go on a lot of hot streaks, you're going to go on some cold streaks and you just try to weather the storm."
Josh Tomlin (5-7) allowed four runs, six hits and a walk over 4 1/3 innings.
Cleveland (50-48) had reached a season-high three games over .500 by winning four in a row.
"It was a great series for us," Tomlin said. "Took three games from them, but I came up short."
Detroit gave Smyly some support offensively, scoring two runs in the first and two more on Torii Hunter's drive deep into the left-field seats in fourth. Austin Jackson led off the first with a double and scored on Ian Kinsler's single. Kinsler came home on Victor Martinez's sacrifice fly.
Indians relievers C.C. Lee and Kyle Crockett stranded a total of five runners by combining to strike out the last two batters in the fifth and the sixth.
Cleveland manager Terry Francona was pleased with his pitcher's performances against Miguel Cabrera, who went 0 for 4, and Victor Martinez, who was 3 of 15 over the four-game series.
"Those guys in the middle are pretty special," Francona said. "And, I thought we did a good job against them."
Nick Castellanos hit an RBI double for a four-run lead in the eighth inning, taking some pressure off Nathan, who was greeted by the fans with a mix of cheers and boos after giving up a game-losing hit in Saturday night's loss.
"I don't think it hurt that he got back out there," Ausmus said.
Tigers RHP Justin Verlander (8-8, 4.88) is to face Arizona LHP Vidal Nuno (0-1, 3.00) when Detroit begins a seven-game trip that continues against the Los Angeles Angels. ... Martinez played first base, giving Cabrera a day of relative rest as a designated hitter, and may play there while Cabrera moves to third for a game or two against the Diamondbacks. ... The Indians will stay on the road, expecting to put called-up LHP T.J. House (1-2, 4.40) on the mound against LHP Kris Johnson (0-1, 5.40) Monday night and called-up RHP Danny Salazar on Tuesday night at Minnesota. ... Detroit and Cleveland optioned the 26th players they had for Saturday's doubleheader, sending RHP Drew VerHagen to Triple-A Toledo and RHP Zach McAllister to Triple-A Columbus. ... Tigers owner Mike Ilitch attended the game on his 85th birthday. ... The Indians had won a season-best five straight on the road. ... Cleveland had won a season-best five straight on the road.
Copyright by STATS LLC and The Associated Press
DETROIT, MI - JULY 20: Pitcher Drew Smyly #33 of the Detroit Tigers pitches against the Cleveland Indians during...