Yankees prospect Eric Duncan homered twice in the contest, belting a solo shot in the third inning and a three-run blast in the seventh.
Hill was the third Grand Canyon pitcher to work, following four innings from Glen Perkins and Ricky Barrett (Twins), and did not allow a hit in the two innings, striking out one.
The 28-year-old righthander came back from Tommy John surgery and split the 2005 season between Class-A St. Lucie and Double-A Binghamton.
Hill was 0-0 with a 2.35 ERA and one save in seven appearances for St. Lucie before joining Binghamton in July, where he was 1-3 with a 4.29 ERA and four saves in 19 appearances.
Surprise – which lost for the first time this season - managed only four hits in the game. New York's Chase Lambin contributed a double to Grand Canyon's 15-hit attack.