Former New Zealand all-rounder Scott Styris was the man who did the damage on his way to a 37-ball century as the hosts piled up 230 for four at Hove.
Sussex reached a total of 230-4 to win the match by 39 runs and qualify for the semi-finals of the competition.
The infamous over, the 18th of the innings, started with two no-balls which both found their way to the boundary, before Styris launched a six to make it 16 runs from one legitimate delivery.
Another maximum was followed by a four, before Fuller finally produced a dot ball and Styris, who had swung lustily and missed for once, thumped the edge of his bat in frustration.
A top-edged hook dropped inches short of the rope before 37-year-old Styris launched the last ball over long-on for six more.
Styris' innings equalled the third-fastest century in t20 history, and nine maximums and five fours meant he ran only 26 of his unbeaten 100.
"I'm just pleased I got a few in the middle," he joked on Sky Sports 2. "I'm just a slogger these days, they all seem to go even when I don't want them to."
Fuller finished with figures of one for 57 off only three overs - Liam Norwell was instead invited to bowl the last over of the innings.