Buttler surpassed West Indian Kieron Pollard's record of 14,803 by hitting three consecutive sixes off Marco Jansen and struck six in total in a 20-ball 51. It carried him to a format total of 14,833.runs.
The ECB classes the Hundred competitions as List-A T20 matches, therefore performances in the 100-ball format count towards overall T20 records.
Chasing 156 for victory, Giants openers Tim Seifert and Paul Walter made a fast start, sharing in a 74-run stand for the opening wicket before the latter was dismissed for 37 off 18 deliveries.
Walter struck two sixes and four fours, while Seifert went on to finish unbeaten on 62, including 10 fours, as he shared a winning 87-run partnership with Buttler.
Super Giants' third win from six matches in The Hundred this season lifts them into a top-three place, four points behind second-placed Fire.
Visiting opener Phil Salt was denied his half-century after being caught by Leus du Plooy off Josh Tongue for a 37-ball 48 and although fellow opener Matt Short made a dominant 71 off 47 deliveries, they were restricted to 4-155.
Later in the day,Trent Rockets moved four points clear at the top of the standings after cruising to a seven-wicket win against Birmingham Phoenix.
Rockets captain Sam Billings struck the winning runs with his third six in a 19-ball 31 not out to steer his side home at 3-116 with 17 deliveries to spare as Phoenix struggled to defend their total on a difficult batting pitch.
Rockets turned in a bowling and fielding masterclass in restricting Phoenix to 6-111, with 29 dot-balls bowled in their first 50 deliveries before the visitors slipped to 3-42 with 48 remaining.
Phoenix wicketkeeper Joe Clarke thumped five sixes and three fours for a 45-ball 62, but Laurie Evans (19) was the only other batter to reach double figures. Aussie opener Mitch Owen lasted only three balls before being caught by compatriot Tim David.
Rockets took a measured approach to their run chase with Ben Duckett (22) and Finn Allen (28) putting on 41 off 38 balls for the opening wicket.
After Aneurin Donald went for 17 to leave Rockets on 2-60 eight balls later, Billings expertly guided his side's run chase.
