PITTSBURGH -- Gerrit Cole pitched six solid innings to run his winning streak to six games and Pedro Alvarez hit a tiebreaking home run as the Pittsburgh Pirates beat the reeling Milwaukee Brewers 5-2 on Sunday to sweep the three-game series.

Cole (2-0) allowed two runs and five hits while striking out six and walking one. The right-hander has not lost since last Sept. 1 against the Cardinals at St. Louis.

The third-year pitcher also improved his career record to 13-6 at PNC Park, where he has made six consecutive quality starts.

The Brewers dropped their fifth game in a row to fall to 2-10, the worst start in the franchise's 47-year history. They scored two runs or less in eight of their 12 games.

The Pirates (6-6) are 5-1 against the Brewers this season, scoring at least five runs in each of the five wins and outscored them 33-17.

Alvarez's solo home run with one out in the third inning off Matt Garza (1-2) put the Pirates ahead for good, 3-2. It was the first baseman's fourth homer of the year as he improved to 9-for-20 lifetime against Garza.

Catcher Chris Stewart added a two-run single in the sixth inning to increase the Pirates' lead to 5-2. That came right after shortstop Jordy Mercer was hit in the right ribcage and was removed from the game.

Right-hander Jared Hughes, left-hander Tony Watson and closer Mark Melancon each pitched one scoreless inning of relief for the Pirates, with Melancon notching his second save.

Garza, who has only one quality start in his last seven matchups with the Pirates, was tagged for five runs and seven hits in six innings. He had three strikeouts and three walks.

Third baseman Josh Harrison had two of the Pirates' seven hits, including a leadoff single in a two-run first inning. Harrison scored on a wild pitch and center fielder Andrew McCutchen followed with an RBI single.

The Brewers evened the score at 2-2 in the second inning. Shortstop Jean Segura, whose five-game hitting streak ended, drove in a run with a ground out, and catcher Jonathan Lucroy followed with an RBI single for the first of his two hits.

NOTES: Milwaukee RF Ryan Braun was back in his usual No. 3 spot in the batting order after hitting leadoff Saturday night for the first time in his nine-year career. SS Jean Segura returned to the top spot as manager Ron Roenicke tries to find a reliable leadoff hitter while CF Carlos Gomez (strained right hamstring) is on the disabled list. ... Brewers 3B Aramis Ramirez, who entered the day hitting just .140, was rested and INF Luis Jimenez started at third base. ... Both teams open four-game series Monday night with Milwaukee playing the Cincinnati Reds and the Pirates facing the Chicago Cubs. ... Brewers RHP Wily Peralta (0-1, 4.50) matches up against Reds RHP Anthony DiSclafani (1-0, 1.38). Pirates RHP A.J. Burnett (0-1, 2.25) squares off with Cubs RHP Jake Arrieta (1-1, 1.98).