Laube also returned four punts for 125 yards with most of them coming on a 92-yarder for a touchdown. The play occurred with 35 seconds left before halftime for a 10-0 lead and New Hampshire never looked back.
The Wildcats (3-1, 3-0 Colonial Athletic Association) built a 24-0 lead before Towson scored. Tyrrell Pigrome threw a 17-yard touchdown pass to Robert Schwob for the Tigers' (2-2, 0-1) first score.
Brosmer finished 17-for-23 passing for 194 yards completing passes to six different receivers.
Pigrome threw for 142 yards for Towson.
New Hampshire has a 7-3 all-time record against Towson with four consecutive wins against the Tigers, including last year's 26-14 victory at Wildcat Stadium.
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