The 18-year-old didn't get off to the best of starts at Flushing Meadows as his opponent from Canada ran out a 6-2 victor in the opening set.
However, Stockport-born Broady responded in the second set by recording a 6-2 success of his own.
That forced the match into a deciding third set that was level at five games apiece. It was then that Broady was broken and Peliwo went on to hold his next service game to claim the title.
Broady is currently ranked 805 in the standings.