© AP Photos
It was the Welshman's fourth successful defence of the WBO belt and his first appearance in America.
Hawk was only confirmed as Cleverly's opponent earlier this week when original challenger Ryan Coyne had to pull out.
The 25-year-old took some heavy shots but used his superior skill and hand speed to extend his unblemished record to 25 fights.
Hawk was down twice in the seventh before a left-hook ended the fight in the next round.
It was the first time the American had been stopped in his 26 bouts.