DETROIT -- It didn't look or sound like a rebuilding team, holding on for a win against a contender.
"Great atmosphere with a good team coming in here," Tigers manager Ron Gardenhire said. "They bring a lot of fans, too, and our fans were just wearing them out.
"It was good stuff, and a big win."
Jordan Zimmermann (6-5) pitched six effective innings for Detroit, continuing Chicago's misery.
The NL Central-leading Cubs were held to one run via homer for the fifth straight game, dropping the last three in the offensive slide. This time, Anthony Rizzo led off the sixth with his 19th homer, falling to his knees as he drove Zimmermann's first pitch over the wall in right.
But that was it once again for Chicago.
"I can't really find too much wrong with how we are playing," Cubs manager Joe Maddon said. "The defense has been great and we're pitching well. We're just not hitting.
"Once a game, we hit our home run and then we don't take advantage of our other chances."
Help could be on the way after the Cubs acquired Daniel Murphy in a trade with Washington before the game. The three-time All-Star missed the start of the season because of knee surgery, but is hitting .340 (35 for 103) since the All-Star break.
The Cubs had one last chance when Albert Almora Jr. drew a two-out walk in the ninth. But Greene struck out Heyward swinging to finish off a 10-pitch at-bat, earning his 27th save in 30 chances.
"It was fun, mainly because I came out on top," Greene said.
Detroit got both of its runs in the first inning against Kyle Hendricks (9-10), who allowed 10 hits and walked one in seven innings.
"I didn't bury the last pitch to Victor Martinez and he went and got it," Hendricks said.
Maddon plans to have a face-to-face meeting with Murphy, hoping to find out how much he can play and trying to diffuse expectations, before putting him in the lineup Wednesday at Detroit.
"I'm not asking for Daniel to come in and all the sudden be this force," Maddon said. "When you get a guy like this of course the natural assumption is he's going to take you to the promised land and I don't want him to think that way."
Cubs: RHP Yu Darvish will miss the rest of the season with a stress reaction in his right elbow. ... SS Addison Russell was scratched with a sore shoulder. "He's been playing through it for a while so we backed off," Maddon said.
Tigers: RHP Michael Fulmer, on the DL since July 20 with a strained oblique, is scheduled to throw 70 pitches somewhere on Friday. Gardenhire would not say where Fulmer will have the outing. ... OF JaCoby Jones is expected to have a three-game rehab assignment this week. He has been on the DL since Aug. 13 with a strained right hamstring.
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