The win moves the 24-year-old from Manchester into contention for a world title shot at the end of the year.
After some trash talk in the buildup, Fury began confidently, keeping his opponent at range and dropping his guard.
He was made to pay as early as the second round, though, when Cunningham, a former Cruiserweight world champion, caught him with a big right hand that sent Fury to the floor.
Fury rose to his feet and shakily saw out the rest of the round before regaining his composure.
Cunningham was still getting through cleanly and often as the bigger man struggled to work out his opponent, before finally in the sixth round, Fury started to put some combinations together.
The 36-year-old American began to look tired and in the seventh round Fury backed him into a corner and landed cleanly. Cunningham managed to escape along the ropes, only to be caught by a huge right hand which saw him counted out.
The win sees Fury improve his record to 21 wins from 21 fights, with 15 knockouts, as he targets a world title fight within the next 12 months.