Hand (1-1) improved his career record as a starter to 5-18. Even with the victory, his winning percentage as a starter (.217) is the lowest in the majors among active pitchers with at least 20 decisions, according to STATS.
Giancarlo Stanton hit a solo homer, his 16th. He has seven of Miami's 14 homers at Marlins Park this year.
Rookie Addison Russell's baserunning blunder helped A.J. Ramos earn his fifth save in seven chances. The Cubs had runners at first and second with one out when Chris Coghlan singled to right, but Stanton fielded the ball and threw out Russell taking too big a turn at second.
Miguel Montero then struck out to end the game.
Marcell Ozuna hit a two-out, three-run double off Kyle Hendricks (1-2) that put Miami ahead to stay in the fifth.
Hand allowed six hits and two runs. The left-hander, who came into the game with a career batting average of .058, also singled and scored.
He has allowed two runs in 11 innings in two starts since joining the rotation when the Marlins lost three starters to injury and illness.
Hendricks gave up four runs in six innings. Junior Lake had a pair of doubles and drove in a run for Chicago.
About half the crowd of 23,789 rooted for the visitors, even chanting "Let's go Cubbies!" But the cheers were for the home team in the fifth, when Miami rallied from a 2-1 deficit.
Hand's hit helped the Marlins load the bases with none out, and Hendricks nearly escaped, striking out Stanton and retiring Justin Bour on a popup. But Ozuna lined the first pitch for a bases-clearing double and a 4-2 lead.
Adeiny Hechavarria, batting for the first time in four days after being sidelined by a sore left shoulder, hit a two-out RBI double in the second to put Miami ahead. Cubs manager Joe Maddon elected to pitch to Hechavarria with a runner on second rather than walk him and let Hendricks face the opposing pitcher.
Chicago scored in the third on back-to-back RBI doubles by Anthony Rizzo and Lake.
The Marlins recalled RHP Kendry Flores from Double-A Jacksonville. He started there but will be used in long relief by the Marlins.
The Cubs played without RF Jorge Soler, who hurt his ankle Monday.