CINCINNATI -- Whenever he closes out a game, Reds lefty reliever and expectant father Amir Garrett likes to make the "rock the baby" motion walking off the mound. Maybe it was more appropriate than usual because for a few moments before Garrett closed out the final two outs of a 3-2 victory over the Cubs at Great American Ball Park, there were some restless moments.

But Garrett got the job done in what's been a huge stretch for the Reds’ bullpen. While completing a three-game sweep of the Cubs, the relievers pitched 10 1/3 scoreless innings while the lineup scored only eight runs.

"What we’ve been doing is a big statement that we’re good, we got this. Don’t worry about it, we got it," said Garrett, who recorded his sixth save of the season. "It’s a wakeup call for us, and we’re finally starting to wake up, do our job to the best of our abilities and help our team win.”

The weak link of the club for most of this season, the Reds’ bullpen has a 1.16 ERA over its last 10 games. And it has happened without Tejay Antone and Lucas Sims, their two best relievers, who are on the injured list. Just about everybody has stepped up, especially midseason acquisition Brad Brach, who has a 0.64 ERA over his last 13 games since June 8.

Brach pitched 1 1/3 innings on Sunday, including the first out of the ninth inning.

"I've seen Brad Brach completely dominate the American League East. I've got nothing but confidence when that guy gets the ball," said Reds starter Wade Miley, who allowed 10 hits but only two earned runs over 6 2/3 innings. “The way our whole bullpen has been throwing as of late, just hand it off to 'em and let them go.”

After Brach notched the first out, Garrett took over and ran into some big trouble with six consecutive balls, including Ian Happ's four-pitch walk. Pinch-hitter Eric Sogard's at-bat began with a 2-0 count, bringing out pitching coach Derek Johnson to visit the mound.

"It was crazy at the beginning of that inning," Garrett said. "Usually when I’m warming up and stuff, I get in my routine and throw those balls straight up and I’m like, ‘Oh my gosh.’ I was like, ‘Something’s wrong.’ D.J. comes out and talks to me, and then I threw a slider and my arm pops, which is a good thing because it didn’t [while warming up] in the bullpen. Then I’m like, 'Now we can go,' because my arm was a little stiff."

Sogard grounded a soft single past third base against the shift. But Garrett got Willson Contreras to hit into the game-ending 5-4-3 double play and then he rocked the baby in celebration.

"To be able to lock it back in, focus and make pitches after that is sometimes even more impressive," Reds manager David Bell said after his team completed a 7-4 homestand.

The Reds have won four in a row -- all in one-run decisions -- to improve to 43-40 and 1 1/2 games ahead of third-place Chicago -- losers of nine in a row. The deficit to the first-place Brewers is seven games after Milwaukee's 11-game win streak ended on Sunday in Pittsburgh.

"They’re the best games to be a part of, really," Bell said of the one-run wins. "Everything that happens matters. I also think they make you a better team going through these games. I think everything about them has been a great step for us as a team."

Cubs starter Kyle Hendricks held the Reds to one run -- on Tucker Barnhart’s RBI double in the second -- over six innings. Cincinnati trailed, 2-1, when the decisive rally kicked off with Eugenio Suárez’s single into left field off reliever Dan Winkler. In a 0-1 count, Kyle Farmer was hit by a pitch for the second time during the game and Barnhart’s single loaded the bases.

Pinch-hitter Tyler Stephenson grounded into a fielder's choice at the plate for the first out, but the tying run was forced home when Winkler plunked Jonathan India with a 3-0 pitch. Against lefty Andrew Chafin and a drawn-in infield, Jesse Winker grounded out to first base. Anthony Rizzo threw to second for the forceout, but Chafin couldn't get to first base in time to complete a double play. Pinch-runner Mike Freeman was able to score the go-ahead run.

"It was a grind, no doubt about it," Barnhart said. "But whenever you can kind of just keep the line moving, it’s huge. Being able to do that was great for us today.”

Up next for the Reds are three games at Kansas City, then seven consecutive games against the Brewers -- four in Milwaukee before the All-Star break and three right after. Continuing this winning roll will be paramount.

"For me, I don’t know if it’s the best stretch of baseball we’ve played. But it’s the stretch of baseball that I think I am proudest of this season with the way everybody has contributed," Barnhart said. "I think that it speaks to the group of people that we have and the group of guys we have that’s on the field for us every day. I think it’s huge for us moving forward.”