MILWAUKEE -- Grand slams by Jay Bruce and Todd Frazier capped off a five-homer day for the Cincinnati Reds, who beat the Brewers, 16-10, Tuesday night at Miller Park.

Shortstop Zack Cozart hit two solo home runs and first baseman Joey Votto added a third as the Reds pounded out 13 hits.

Right-hander Jason Marquis gave up five runs on nine hits over five innings but struck out eight and earned his first victory of the season.

Milwaukee infielder Elian Herrera hit his first career grand slam and catcher Martin Maldonado belted a two-run shot as the Brewers offense generated a season-high 10 runs on 12 hits.

Brewers starter Mike Fiers lasted only four innings and was done in twice by two-out mistakes.

Fiers notched his first three strikeouts in the second inning then picked up No. 4 to open the third before center fielder Billy Hamilton bounced out to the mound.

But Votto followed with a base hit, Frazier drew a walk and second baseman Brandon Phillips reached on an error by third baseman Jason Rogers loading the bases for Bruce, who belted a 1-2 fastball to put the Reds up, 4-0.

Milwaukee's offense, though, showed flashes of life in the bottom of the inning. Maldonado, starting in place of the injured Jonathan Lucroy, sliced the deficit in half with a two-run home run, his first of the season.

Shortstop Jean Segura and Herrera recorded back-to-back doubles to make it a 4-3 game and right fielder Ryan Braun tied it up with an RBI single, but was thrown out trying to get to second base.

The momentum was shortlived, though, as Fiers gave up back-to-back singles to open the fourth and, after a fielder's choice by Marquis and a pop out by Hamilton, he left a cutter up to Frazier, who crushed it to left to make it an 8-4 game.

Cincinnati blew the game open against right-hander Tyler Thornburg in the fifth, on an RBI single by catcher Brayan Pena and Cozart's second home run of the series.

NOTES: The Brewers placed C Jonathan Lucroy (fractured left toe) and 2B Scooter Gennett (cut on left hand) on the 15-day disabled list and promoted C Juan Centeno and INF Elian Herrera from Triple-A Colorado Springs. Herrera was not on Milwaukee's 40-man roster, so the team designated Colorado Springs RHP Brandon Kintzler for assignment. ... C Devin Mesoraco returned to the Reds. He left the team during Sunday's game at St. Louis and initially didn't travel to Milwaukee because of what Reds manager Bryan Price said were "family issues." Mesoraco hasn't played since sustaining a hip injury April 12, but he said he was available to pinch-hit Tuesday. ... With his team batting a collective .208 -- the second-lowest average in all of baseball -- Brewers manager Ron Roenicke canceled batting practice. ... Price apologized Tuesday for the language he used in a profanity-laden tirade during a media session Monday.