Arias then shot a grounder to third baseman Rolen, who was handcuffed by a tough hop. He picked it up but his throw to first was late, allowing Posey to score the decisive run.
Sergio Romo (1-0) recorded the final six out to earn the win for the Giants, who still trail the Reds 2-games-to-1 in the best-of-five NLDS.
Cincinnati starter Homer Bailey held San Francisco to just one hit and a run over seven complete innings.
The Reds will again look to advance when they host Wednesday's Game 4.
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