Dunn issued a lead-off single to John Buck before retiring the next three batters to end the game.
Alvarez (2-1) allowed two runs and six hits in 7 1-3 innings. He is 2-0 with a 1.33 ERA in his last four starts.
Marisnick homered off of Jenrry Mejia (1-1) in the second inning to give the Marlins a 1-0 lead. The 22-year-old rookie was hitting .179 (5 for 28) in his first eight games before the home run.
CUBS 6, BREWERS 1
CHICAGO (AP) — Edwin Jackson pitched eight solid innings, David DeJesus drove in three runs and Chicago beat Milwaukee to salvage the finale of the four-game series.
Anthony Rizzo hit a two-run homer and Starlin Castro belted a solo shot as Chicago closed out a 14-13 July, its first winning calendar month since it went 15-10 last July. Jackson allowed one run and eight hits in his longest outing of the season, staying in the game after a 66-minute rain delay in the sixth inning.
Jonathan Lucroy had two doubles for Milwaukee, driving in Rickie Weeks with a grounder down the first-base line in the eighth. Jeff Bianchi and Caleb Gindl also had two hits apiece.
Rizzo went deep in the third, driving a 3-1 pitch from Wily Peralta (7-11) over the wall in center for his 15th homer — matching his career high set a year ago. Castro connected an inning later, making it 3-0 with a drive to the bleachers in left.
Jackson (7-11) struck out four and walked none. The right-hander finished July with a 3-1 record and a 1.83 ERA in five starts.
LOS ANGELES (AP) — Pinch-hitter Lyle Overbay singled in the go-ahead run with two outs in the top of the ninth inning, helping New York defeat Los Angeles.
Overbay singled on a 1-2 pitch from Paco Rodriguez. Robinson Cano scored after reaching on a fielder's choice groundout.
The Yankees added two more runs on an error by Dodgers second baseman Mark Ellis.
Ronald Belisario (4-6) got two outs in the ninth inning, but took the loss. He walked Derek Jeter and pinch-hitter Ichiro Suzuki, who both scored after Belisario was relieved by Rodriguez.
Boone Logan (3-2) got the win in relief.
Mariano Rivera pitched the ninth to earn his 34th save in 36 chances in his farewell season.