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.
Setting sights on spring training, Jose Altuve confident embattled Astros will 'be in World Series'
While second baseman Jose Altuve was open and eager to address the sign-stealing scandal at the Astros' winter fan festival, third baseman Alex Bregman was stoic and stingy with his words as the team sets its sights on spring training.
Cardinals' Harrison Bader confident he'll start in center field this season
Harrison Bader is confident he'll be in center field for the St. Louis Cardinals when the season begins. "It's my position. I'm going to take it. There's no sense in talking about it," he said.
Hall of Fame says deceased players on MLB's ineligible list won't be on ballots
The Baseball Hall of Fame on Saturday said that death does not open the door for players on MLB's ineligible list to be placed on the ballot for entry into Cooperstown.
Altuve, Bregman mum on cheating allegations
Alex Bregman and Jose Altuve decline to comment about the Astros' sign-stealing scandal, but Altuve predicts that the Astros will return to the World Series.
Martinez confident Red Sox will be cleared
J.D. Martinez says MLB's investigation of the Red Sox will find no sign stealing.
J.D. Martinez confident Red Sox will be cleared in investigation, as 'there was nothing going on here'
At the Red Sox Winter Weekend fan festival, Boston slugger J.D. Martinez reiterated his confidence that his club will be cleared in MLB's investigation into sign stealing.