Gary Hooper netted a hat-trick as Scunthorpe made it three wins on the trot.
Martyn Woolford marked his first Scunny start with a close-range goal from Garry Thompson's pass after just three minutes.
Hooper doubled their advantage in first-half injury time from close-range and completed his hat-trick with two right-footed shots after 54 and 67 minutes. The Seagulls grabbed a consolation goal when substitute Jake Robinson headed in Dean Cox's cross after 74 minutes.