It went down to the wire with Hyman taking the championship, 400-390, with a strike and nine-spare in the last two frames.
Clutario settled for the silver medal even as she automatically advanced to the two-game final by topping the grueling 16-game round robin series Friday.
Hyman earned her place in the final by outpointing Korean Lee Uen Ock, 189-147, in the first part of the stepladder stage.
The Filipina gained a one-pin advantage in the first game, 206-205, but ran into severe problems in the second to fourth frames of the second game with horrible splits. Hyman built up a 30-pin lead by the fifth frame and the top step of the champions podium looked pretty well reserved.
But three strikes in a row from the seventh frame brought Clutario back into contention. An eight-spare and a strike capped the Filipinas second-round 184.
Hyman struck in the ninth frame and only had to score a further nine to secure the gold medal. A strike and nine-spare for 195 sealed the issue.