Turner (2-0), making his 19th career start and sixth this season for the Marlins, allowed just one walk while striking out seven.
The right-hander threw 77-of-111 pitches for strikes as Miami rebounded from a 9-2 loss in Friday's series opener.
Giancarlo Stanton socked a solo homer for the Marlins while Jeff Mathis capped a three-run fourth inning with a two-run single.
Eric Stults (6-6) was charged with the loss, giving up six runs (five earned) on seven hits over 3 2/3 frames.
Nick Hundley went 2-for-3 with an RBI for the Marlins.