Gold gave DePauw its first goal at the 25:13 mark following a foul and after receiving a pass from Jack Cornelo.
In the second half, Brady scored in his first game as a Tiger at the 60:51 mark. Justin Mitchell was credited with the assist after his shot was deflected and found Brady's foot.
Davis made three saves for his first shutout. DePauw outshot Hanover 13-6 but had two yellow cards to Hanover's one.
DePauw (1-0) returns to action Sunday when they face Case Western Reserve in their home opener.