Beaumont's score is the highest in the men's and women's Hundred tournaments while the Fire's total of 181-3 also set a women's record.
Will Jacks' 108 not out for Oval Invincibles last year was the previous highest score in The Hundred.
"I don't know what just happened to be honest," Beaumont told Sky Sports.
"I just had an absolute day out. It was great to put on a show for the fans."
The English batter, who hit 20 fours and two sixes in her 61-ball innings, survived when she was dropped on 32 while successfully challenging a leg-before decision on 75.
The Welsh Fire captain has now scored centuries across four different formats.
In June, Beaumont became the first Englishwoman to score a double century in test cricket, scoring 208 - the fifth-highest score in women's tests - against Australia in the women's Ashes.