The highly visible success of Page, a star reliever for three Yankee World Champions, hastened the widespread use of the relief specialist. Page succeeded Johnny Murphy as the Yankee bullpen ace, and while not as good or as durable as Murphy, he worked more games per season. In 1949 (although the statistic did not officially exist at the time), he set a ML save record of 27 that stood until 1961, and his 14 relief wins in 1947 was the AL record until Luis Arroyo broke that one too in 1961. He led the league twice each in saves, relief wins, and appearances (but three times in relief losses).
Page spent his first three seasons as a struggling starter before Bucky Harris put Page into the bullpen in 1947. Page had just two starts that year and one final start in 1948, and he went 14-8 with 17 saves and a 2.48 ERA (2.15 in relief). Page saved Game One of the 1947 World Series, lost Game Six, and won the clincher, holding the Dodgers to one hit in five scoreless innings. In 1949 he was even better, saving the record 27 while going 13-8 with a 2.59 ERA. In the World Series, he won Game Three and saved the clincher. He dropped off the next year and failed in a comeback attempt with the Pirates in 1954.