Scutaro sent a 2-1 pitch from Santiago Casilla (0-2) into the left-field seats to give Colorado the lead after the Giants scored three times in the seventh to tie the score.
The late heroics gave the win to Rex Brothers, who pitched the eighth. Rafael Betancourt put two runners on in the ninth but held on for his seventh save.
Melky Cabrera drove in two runs for the Giants and Angel Pagan had three hits and an RBI.
Tim Lincecum allowed four runs on seven hits and struck out seven in seven innings for the Giants, whose three-game winning streak came to an end.