Bayron, 27, finally found his touch after three days of struggle, gunning down seven birdies against two bogeys at Stellenbosch Golf Club for a 34-33 card highlighted by three straight birdies from No. 15.
With Marvin Dumandan carding a 74, the Philippines went under-par for the first time after two 154s and a 150 in the three-to-play, two-to-count format event, finishing with 141-599 and improving four rungs for a 38th place finish in the Eisenhower Cup.
Michael Bibat, who counted in the first and third rounds, withdrew in the fourth round due to low blood pressure.
Dumandan actually made a birdie-par-eagle from No. 6 to negate a string of bogeys from No. 2. But the spearhead of the team, backed by ICTSI, dropped two strokes in the first two holes at the back and never recovered for that two-over card.
But the day belonged to the Dutch, who bested first round leader Canada and foiled the United States bid for a fourth straight championship with a solid final round performance at De Zalze.
Joost Luiten fired a 67 while Wil Besseling shot a 70 to power the Netherlands to the victory on a final round output of 137 for a 554.
That was two strokes better than Canada, which also made a 137 for a 556 while the Americans, champions in the last three editions of the biennial event, made a 138 and finished third with a 557.