Paul Janish added two hits and drove in a run for the Reds, who just wrapped a 2-8 trip to Cleveland, Philadelphia and Atlanta. Wood (4-3) allowed three runs and seven hits over six innings in the opener of a 10-day, nine-game homestand.
The defending NL Central champions gained a game on the teams ahead of them in the division, the Brewers and first-place St. Louis, which lost at home to San Francisco.
"When you get a chance to catch the teams ahead of you and you do it, it's nice," said Bruce, who also tripled for the first time this season and had a base hit. "We did a good job tonight. I wasn't overly concerned about the cycle. It is what it is. I just wanted the win."
Bruce hit his NL-best 16th homer in Cincinnati's four-run fourth inning. He is batting .405 with six homers and 17 RBIs in his last nine games, and .346 with 12 homers and 32 RBIs this month.
Manager Dusty Baker wanted to see Bruce complete the cycle.
"I wanted him to get that double out of the way," Baker said. "It sure is nice to see him hitting. I just hope he accepts what he's doing and doesn't wake up."
The Brewers, who went 8-1 on their last homestand, dropped to a National League-worst 8-18 (.308) on the road, including 0-4 this season and 1-11 over the last two years in Cincinnati. They are 1-6 against the Reds this season and 4-17 over the last two years, a trend that is starting to disturb manager Ron Roenicke.
"The more things happen on the negative side, the more it gets in your head a bit," the first-year manager said.
Wood (4-3) struck out two and walked none. He is 3-0 with a 3.33 ERA in four career starts against Milwaukee over the last two years.
"I felt good," Wood said. "I felt like my pitches were working pretty well. I would like to have gone a little deeper into the game, but I'm glad that I was able to hold them off."
Bruce tripled and scored on Jonny Gomes' sacrifice fly in the second against Narveson, who is 0-3 with a 7.06 ERA in six career games against Cincinnati. Two innings later, following Joey Votto's second walk in as many plate appearances and Scott Rolen's single, Bruce launched an 0-2 pitch 422 feet into the right-field seats.
Narveson was upset with allowing Rolen, Bruce and Gomes off the hook after getting two strikes on each of them.
"I left a pitch up to all of them," the left-hander said.
Gomes followed the homer with a double and scored on Janish's single.
"They hit some pretty good pitches," Wood said. "Gomez went down and got it. I wanted to throw a cutter in to Wilson and it was in. They just put some good swings on them."
Narveson (2-4) lasted only four innings, allowing five runs and five hits.
The Reds tacked on two more runs in the sixth with help from the Brewers. With two out and runners on first and second, pinch-hitter Fred Lewis had an RBI single and Janish scored on a throwing error by catcher Jonathan Lucroy.
The Reds' eight losses on their last road trip were the most since they lost eight on a 12-game trip from June 20 through July 3, 2003. They lost eight games on a 10-game trip for the first time since April 15-25, 1996. ... Cincinnati didn't make it official, but RHP Chad Reineke is the projected starter Tuesday against Milwaukee. The appearance will be his first in the majors since starting for Oakland against Texas on Aug. 5, 2009. Reineke is 5-2 with a 2.52 ERA in 10 games, nine of them starts, with Triple-A Louisville. ... Milwaukee RHP Takashi Saito, on the 60-day DL with a strained left hamstring, was expected to throw in the bullpen Tuesday and three or four more times after that before trying a simulated game, Roenicke said.