"This is awesome," Zambrano said after improving his record to 2-2. "We come every day to play ball. Everyone here is having fun, not only in the game, but after the game. When we come here to the clubhouse, everyone is having fun."
The Marlins are 13-4 in May, and 2-1 on their road trip.
Friday's comeback win got Miami off to a good start in Interleague Play, where the franchise is 136-117 since the concept was introduced in 1997.
Zambrano minimized the damage on a night just 52 of his 110 pitches went for strikes. Still, the veteran was able to stay out of big trouble because he yielded just four hits.
"I felt good. Everything was working," Zambrano said. "The sinker was running good. I gave up two runs, but that doesn't stop me to battle and throw seven strong innings."
In his last four starts, Zambrano has an ERA of 0.90, giving up three earned runs (four total) in 30 innings.
The victory was locked down by Bell, who collected his first save since May 1.
It's been a rough year for Bell, who has saved four of his eight chances. His last save opportunity was on May 4 at San Diego.
Despite Bell's struggles, Zambrano has remained supportive of the three-time All-Star closer.
"He was good today," Zambrano said. "He was throwing strikes. That's the Heath Bell we want to see. He's had some struggles. I think if we support him and we give him a hand, he will be OK. He will be good."
In recent weeks, Bell has discussed dealing with struggles with Zambrano, who had some rough years in Chicago.
"I've talked to him numerous times," Bell said. "He's had some bad seasons, and how he deals with it. He's a veteran player to me. He's been there for me from Day 1."
Cleveland's Justin Masterson also allowed two runs in seven innings, taking a no-decision.
The Marlins battled back from two runs down early, and they took the lead in the eighth, capitalizing on an error.
Ramirez's sacrifice fly off Joe Smith scored Bryan Petersen with the winning run.
Reliever Tony Sipp opened the inning by walking Petersen. After Jose Reyes' bunt moved Petersen to second, Omar Infante tapped the ball back to the mound. Petersen raced back to second and Smith's throw there deflected off the Miami runner, allowing him to move to third.
"He probably took too long to get rid of the ball," Indians manager Manny Acta said. "When you get the guy caught in between, give it up and get him. But once you don't throw the ball right away, then you just get the out at first base and now you have two outs and a runner on second."
Petersen felt he made an aggressive read on the grounder.
"I didn't feel I was too far off where I was in no man's land," he said. "I was like, 'All right, I'll try to make it back in.' I felt like I could have beaten the throw, even if it was a good throw. Whatever happened, the ball went into right, and I got to third."
After falling behind by two runs in the second inning, the Marlins tied it at 2 in the sixth. Infante reached on a one-out walk, and he moved to third on Ramirez's double off the wall in left. Greg Dobbs' sacrifice fly to left scored Infante.
The Indians capitalized on a pair of two-out walks by Zambrano and scored twice. Johnny Damon got the rally started with a walk, and he scored on Casey Kotchman's double down the right-field line. After Jose Lopez walked, Shin-Soo Choo lined an RBI single to center.
In the third inning, the Marlins cashed in on a leadoff walk by Petersen. On a hit-and-run, Reyes singled to right, advancing Petersen to third. Infante's fielder's-choice grounder to short scored Petersen.
The run snapped Miami's scoreless innings streak at 13.
In the fifth inning, Emilio Bonifacio had his Marlins' record string of 21 straight steals snapped when he was thrown out by Carlos Santana. Bonifacio opened this season 20-for-20.
Bonifacio, who hasn't missed a game all year, was shaken up on the slide. He sprained his left thumb and was replaced in the bottom of the fifth.
Bonifacio's string of 112 consecutive games is the third longest in the National League, and it's now in jeopardy.
He will be examined on Saturday morning.
Miami paces the Majors in stolen bases. But Santana threw out three of four runners on the night. It was the first time the Marlins have had three caught stealing in the same game since Aug. 25, 2006.
Because of the pitching of Zambrano, the Marlins were able to collect a win on a night they scratched out just enough offense.
"Zambrano did a good job of expanding the zone on some of those guys," Acta said. "He did good. He pitched well and we couldn't get those guys in the middle to do anything to him."