After Ehire Adrianza laid down a sacrifice to move the runners up, pinch-hitter Buster Posey was intentionally walked to load the bases.
That brought up Scutaro (2-for-4), who lined a single to right, chasing home Crawford with the score-tying run and sending Pagan to third.
Belt then followed with the key blow, slapping an RBI hit the opposite way to left field.
Guillermo Moscoso (2-2) tossed two shutout innings to notch the decision and Santiago Casilla secured the victory with his second save.
Nelson Arenado supplied two RBI for the Rockies.