Grimm walked Frazier and left a pitch up to Bruce, costing Chicago the game.
Frazier connected for the first time since he won the All-Star Home Run Derby, and later scored on Bruce's key two-run shot Monday night, powering the Cincinnati Reds to a 5-4 victory.
The Reds hit three homers in all, including Marlon Byrd's solo shot, and beat the Cubs at Great American Ball Park for the first time this season. Bruce's drive off Grimm (1-3) put Cincinnati up 5-4 and spoiled manager Joe Maddon's decision to bring him in.
''That falls under the category of it being the right thing to do, but it just didn't work,'' Maddon said. ''I felt pretty good about it.''
Grimm walked Frazier to bring up Bruce, who hit only the second homer allowed by the reliever this season.
''I was just trying to attack Frazier,'' Grimm said. ''It didn't work out.''
Ryan Mattheus (1-1) pitched a hitless inning for Cincinnati in relief of Michael Lorenzen. J.J. Hoover escaped a threat in the eighth. Aroldis Chapman pitched the ninth - a day after he threw a career-high 44 pitches - and retired the side on 13 pitches for his 19th save in 20 chances.
The Cubs are 7-3 against Cincinnati this season, including 2-1 at Great American. They haven't won their season series since 2009.
Frazier won the derby at Great American last Monday night, hitting the clinching homer with his final swing. Those 15 minutes of aiming for the seats tired him out - he was 0 for 3 in the All-Star Game and hitless in 10 at-bats during a series against Cleveland over the weekend.
His solo shot in the first inning off left-hander Clayton Richard was his first homer since June 28th and his first at Great American since June 21. He has hit 16 of his 26 homers at home.
The Cubs' Kris Bryant and Anthony Rizzo also participated in the All-Star derby and helped them pull ahead 4-3. Rizzo had a sacrifice fly, and Bryant doubled home a run. Jorge Soler's two-run double put Chicago ahead in the fifth.
The teams firmed up their pitching plans for Wednesday's day-night doubleheader, which makes up a game rained out in April. The Cubs will go with Kyle Hendricks and Dallas Beeler. The Reds will start Mike Leake and Tony Cingrani.
Brandon Phillips went behind second base to get Jorge Soler's grounder in the seventh, and then flipped behind his back for a barehanded force out by shortstop Eugenio Suarez at second, ending a Cubs threat.
Cubs catcher David Ross was ejected by plate umpire Paul Schrieber for arguing from the dugout in the seventh inning.
Cubs catcher Kyle Schwarber batted second and went 1 for 4 with a single. The rookie is from nearby Middletown, Ohio, and played at Great American for the first time eight days earlier, winning the MVP award in the All-Star Futures Game.
Cubs: LHP Zac Rosscup flew to Double-A Tennessee on Monday to continue his rehab stint at a higher level. Rosscup, on the 15-day DL since June 17, had been pitching with the rookie team in Mesa, Ariz.
Reds: LHP Manny Parra went on the 15-day DL with a strained elbow. ... Mattheus twisted his left knee while fielding Starlin Castro's grounder in the 6th but stayed in the game after a few practice throws.
Reds: Raisel Iglesias (2-5) makes his second start since returning from a strained left oblique. He gave up five runs and eight hits in only 4 1/3 innings of a 14-3 loss at Miami on July 11.
This version of the story has been corrected to show that Grimm is a right-handed pitcher.
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