Nolasco (9-6) improved to 6-2 on the road this season, turning in a seven-inning performance in which he allowed two runs on six hits with six strikeouts.
Clay Hensley worked a perfect eighth and Leo Nunez produced a 1-2-3 ninth for his 19th save.
Uggla singled in Florida's first run during a two-run third and his infield base hit in the seventh delivered another score to give the Marlins a 3-1 lead.
Dan Haren (7-7), who had been looking for his first victory since June 12, took the loss. He gave up three runs on 10 hits in 6 2/3 innings.
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