Suarez had given Cincinnati a 4-1 lead when he took Adrian Houser deep with two out in the seventh.
The Brewers took the lead right back an inning later when Tyler Saladino connected on a first-pitch fastball from Rasiel Iglesias for his second grand slam in as many days, snapping an 0-for-8 drought with runners in scoring position for Milwaukee.
With Josh Hader unavailable after working in each of Milwaukee's last two contests, Jeffress (3-3) got the call for the ninth. He struck out pinch-hitter Derek Dietrich to open the inning before giving up a single to Nick Senzel, putting the tying run aboard.
Senzel moved to second on Joey Votto's groundout to bring up Suarez, who sent Jeffress' second offering, a fastball right down the middle, to left for his ninth home run of the month and 26th of the season.
Reds starter Sonny Gray went six innings and allowed just a run on four hits and two walks while striking out seven. He's allowed two or fewer runs while working at least six innings in each of his last five starts.
Right-hander Chase Anderson struck out six over 5 2/3 innings for Milwaukee. He was charged with two runs on seven hits and two walks and took no decision for the fourth time in his last five starts.
Reds: RHP Tyler Mahle was placed on the 10-day injured list with a strained hamstring Monday, three days after suffering the injury while throwing his very last pitch in an outing against the Cardinals. RHP Sal Romano was recalled from Triple-A Louisville to replace Mahle on the roster while Lucas Sims will take Mahle's spot in the rotation Wednesday against the Brewers.
Brewers: Milwaukee put RHP Brandon Woodruff on the injured list Monday after an MRI revealed a strained left oblique, leaving him sidelined for least six weeks. Woodruff suffered the injury Sunday in a start against the Diamondbacks. ... 2B Keston Hiura was scratched from the starting lineup before the game with a sore quad but appeared as a pinch-hitter in the eighth, drawing a four-pitch walk before he was replaced by a pinch-runner.
The series continues Tuesday night with Reds RHP Tanner Roark (5-6, 3.97 ERA) facing off against Milwaukee RHP Zach Davies (8-2, 2.79). Davies has a 0.77 ERA over his last four starts while Roark is 1-0 with a 4.24 ERA in four starts against the Brewers this season.
With another ninth-inning nightmare, Cubs' road woes could be their undoing
Two straight devastating walk-off losses in Philly and Pittsburgh make it clear: If the Cubs can't find a way to win away from Wrigley, they won't find their way into October.
Montgomery outpitches Syndergaard as Royals top Mets 4-1
Mike Montgomery outpitched Noah Syndergaard, and the Kansas City Royals ended their scoreless drought Friday night in a 4-1 victory over the New York Mets.
Rockies use strong outing by Jon Gray to beat Miami 3-0
Jon Gray struck out seven in eight strong innings and Nolan Arenado and Ryan McMahon homered for the second straight game, leading the Colorado Rockies to a 3-0 win over the Miami Marlins on Friday night.
Homers by Kepler, Schoop lead Twins past Rangers 4-3
Max Kepler and Jonathan Schoop hit two-run home runs to lead the Minnesota Twins to a 4-3 win over the Texas Rangers on Friday night.
Kepler, Schoop homer to beat Rangers in Arlington
Max Kepler hits a home run to right field in the fourth inning and Jonathan Schoop hits one to right in the seventh to lift the Twins over the Rangers.
Bellinger hits 41st homer, Dodgers beat Braves 8-3
Cody Bellinger hit his 41st home run, Max Muncy and Justin Turner connected against reliever Sean Newcomb in the seventh inning, and the Los Angeles Dodgers beat the Atlanta Braves 8-3 Friday night in a matchup of NL division leaders.