The D-backs built a 5-2 lead and were still ahead, 5-3, in the seventh, when Hinch took Haren out of the game.
Haren, who woke up with an upset stomach, threw 112 pitches and had run the bases twice in the game and appeared to be spent.
"I didn't feel great, but I got through it and gave it all I could," said Haren, who allowed three runs on 10 hits over six frames.
When asked if he thought he could have continued to pitch, Haren backed Hinch's decision to take him out.
"I then what, throw 130?" Haren said. "Probably not the smartest thing. I've been pushed a little bit so far this year and I don't think A.J. is going to go out there and let me throw 140 pitches at the beginning of May."
It didn't take long for the Cubs to get to take advantage of the Arizona relievers.
Right-hander Bob Howry allowed a one-out single to Marlon Byrd and then gave up a two-out two-run homer to Alfonso Soriano to tie the game at 5.
"I don't know how to explain it," Hinch said. "It's hit everybody. It hasn't been one or two particular guys -- experience not experienced -- it's a collective group that needs to regain their competitive edge and their conviction to getting outs and helping this team."
It only got worse from there.
Juan Gutierrez came in to pitch the eighth, and after a leadoff single, he wound up walking the bases loaded.
"I couldn't locate my pitches very well," Gutierrez said.
Derrek Lee made Gutierrez pay when he hit a sharp single into left field past a diving Mark Reynolds to score a pair of runs.
"You've just to throw strikes, man, you can't walk guys and keep giving teams chances," Reynolds said. "We have to find a way to overcome it. It's not like a bad outing here or a bad outing there, it's become a consistent thing. I feel like we're scoring a lot of runs and giving ourselves a chance to win pretty much every game we've played this year. It's just the walks and we're not making the key pitches in the key situations and it's frustrating."
The D-backs bullpen entered the game with the worst ERA in the National League at 6.85, nearly a full run worse than the next closest team.
"I would rather get blown out 25-0 than to have the lead and lose it at the end," Reynolds said. "We've been up pretty big the past four or five games and we're what, .500? It's almost like you have to put teams away by 10 runs in order to win games. We've got some guys down there that have proven themselves, the veterans, I keep saying I hope they snap out of it. I hope they do it for the sake of the team and for the sanity of a lot of guys in here."
While he obviously wants to see his bullpen pitch better, Hinch was not pleased with other aspects of the team's play Saturday.
"Today we got what we deserved," Hinch said. "We didn't play clean defense, we didn't throw strikes out of the bullpen, didn't keep the ball in the ballpark. It's bad baseball for the latter half of the game for sure."