"We got out of some very tough situations," Baker said. "A win is a win."
And this one was the third straight for the defending NL Central champions.
After Chicago scored a run in the sixth to pull close, reliever Sam LeCure, who's also started four games this season, retired three straight with the bases loaded and no outs.
"We made it tough on ourselves. I think we just tried to keep the crowd, the Reds fans, on the edge of their seats," Phillips joked.
Phillips made a nice play behind second and a great behind-the-back flip to shortstop Edgar Renteria for a force out in the third inning, caught Alfonso Soriano's sinking liner to start a rally-busting double play in the fifth and also had an RBI single.
"All I try to do is catch the ball and be the pitcher's best friend. Try to make plays," said Phillips, the Reds' Gold Glove second baseman.
Edinson Volquez (3-1) got the win, laboring through numerous jams in five-plus innings. He allowed six hits and four runs, walked four and threw a pair of wild pitches.
"At the beginning of the game I thought it was going to be a different game. But then in the fourth inning I started losing my fastball command," Volquez said.
Matt Garza (1-4), the Cubs' biggest offseason acquisition, still has one win in his first seven starts and none in four outings at Wrigley Field. He gave up six hits and five runs in six innings.
"I felt like it was going to be a good day," Garza said. "They did a great job of just extending innings. In that fourth inning (Joey) Votto puts his bat out there and hits the ball up the middle. And then Phillips the same thing, just throws his hands out, a seeing eye single through the right side. Just bear with it and go with it."
Bruce's seventh homer of the season was a high drive into the right-field bleachers with the wind blowing out and gave the Reds the lead for good in the fourth at 3-1. It was the first homer surrendered by Garza this season.
"Garza had good stuff. For the most part he pitched well. He just made a few mistakes and we had some good at-bats when we needed them," Bruce said.
The Reds added on in the top of the fifth on those two-out RBI singles by Votto and Phillips. Paul Janish started the inning with a hustling double after his hard grounder went off shortstop Starlin Castro's glove. With two outs and Janish at third, Garza walked Renteria before Votto and Phillips delivered to make it 5-2.
Barney, Castro and Aramis Ramirez reached Volquez for consecutive one-out singles to make it 5-3 in the bottom of the fifth, but the inning fizzled when Phillips made a nice grab of Soriano's sinking liner and flipped to Renteria to double off Castro.
The play was close, but second base umpire Jerry Layne called Castro out.
"Not sure we didn't get a bad break there," Cubs manager Mike Quade said.
"Tell you the truth, I think I got him, but I heard how the crowd went crazy and they made it seem like I didn't," Phillips said. "The only thing I can really say is thank you to the ump."
Geovany Soto greeted LeCure with an RBI single in the sixth, cutting it to 5-4. LeCure then hit pinch-hitter Reed Johnson to load the bases before striking out Fukudome, retiring Barney on a popup and getting Castro on a bouncer to short.
The Cubs also loaded the bases in fourth but scored once on Soto's double-play grounder.
Garza was 0 for 25 in his career, including 0 for 14 this season, before collecting his first major league hit in the second, a sharp single to center that set up the Cubs' first run.
Fukudome then grounded to first baseman Votto, whose throw to second was dropped by Renteria for an error. Phillips then made his play behind second, flagging down Barney's hopper and flipping the ball behind his back to Renteria — while still on the ground.
Notes: Bruce has five homers in his last 10 games. ... Votto has reached base in all 32 of the Reds' games this season. ... Castro is 2 for 21 over his last five games. He flied out to end the game.