Cueto's pitching line was misleading, considering the quality of his effort. In 6 2/3 innings, he was charged with five runs (four earned) on eight hits with two walks and six strikeouts.
Meanwhile, Zambrano was dominant for eight innings, during which he faced just one over the minimum batters and struck out five.
"He had us going at balls a little bit out of the zone and taking balls in the zone," Reds manager Dusty Baker said. "That's Zambrano. He threw a great game tonight."
Dunn's full-count homer to the right-center-field bleachers gave the Reds a 1-0 lead in the second inning. It was the Reds' lone hit off of Zambrano (10-3), who retired his final 20 in a row. Only three of the outs went into the outfield.
"Tonight he was really, really good," said Dunn, who has 23 homers this season. "The pitch that I hit was probably the only mistake he made the entire game. That was probably the best I've seen him in a long time."
The only other batter that made Zambrano really work was Cueto, who battled in an 11-pitch at-bat before he grounded out in front of the plate in the sixth.
"That was the best at-bat of the night," Baker said.
The Reds didn't help Cueto defensively as they committed more errors (three) than they had hits (two). Chicago evened the game in the bottom of the second when Mark DeRosa's one-out grounder took a high hop over shortstop Jeff Keppinger's glove for an error. It scored Geovany Soto from second base.
Throwing between 94-96 mph much of the night, Cueto (7-9) also had Cubs hitters guessing wrong. In the fourth, he struck out Reed Johnson with a 77-mph off-speed pitch and appeared poised to match Zambrano the rest of the way.
"I was feeling strong today," Cueto said. "My fastball [velocity] was higher than before. I was locating my pitches good."
That changed in the sixth when leadoff batter Aramis Ramirez hit a first-pitch fastball into the left-center-field bleachers and broke the 1-1 tie.
The game came apart for the Reds in the three-run Cubs seventh as nine batters came to the plate. On Kosuke Fukudome's long drive to the left-field warning track, Dunn got turned around trying to make the catch as the ball dropped in for an RBI double.
"I was playing in because I didn't want anything to drop in front of me," Dunn said. "I didn't take my eyes off of it. I knew he hit it pretty good. I didn't want to lose it in the lights or anything else."
Derrek Lee's single through the left side scored Fukudome for a three-run Reds deficit and ended Cueto's night. Ramirez's double to the center-field wall off David Weathers broke the game open.
"He made one mistake all night, basically to Aramis Ramirez," Baker said of Cueto's game. "The ball got over the plate. Other than that, he pitched masterfully. I tried to get him the last out so he could get a chance to win. He threw the ball great tonight."
A critical six-game road trip that was intended to get the Reds back to respectability is off to a rough 0-2 start. Like his team, Cueto was trying to get back to a .500 record after some inconsistencies earlier in the season. He had pitched much better lately and won his previous two outings with strong quality starts.
Another would-be solid performance was wasted this time, however.
"His job is to pitch, not hit. Our job is to hit," Baker said. "[Zambrano] threw the ball well tonight. I've seen that many, many times. That score wasn't indicative to how close that game really was."