The result was a blow for Australia's Jason Behrendorff whose tight opening spell looked to have put the Invincibles on the way to victory.
Dropped from England's white-ball sides this year, Livingstone delivered a reminder of his enduring class with 69 not out off 27 balls at Edgbaston on Tuesday, including an astonishing takedown of Rashid Khan.
Livingstone thumped 26, including three of his five sixes, in Khan's final set, with the vaunted Afghanistan legspinner's 0-59 the worst figures ever recorded in the men's competition.
Saqib Mahmood took two wickets in two balls to set up a grandstand finale, but Benny Howell drove for four first up to settle a high-scoring thriller as a pursuit of 181 was reeled in with two deliveries to spare.
As well as a special innings from captain Livingstone, Birmingham, who started their campaign by losing to Trent Rockets and Southern Brave, were grateful for 51 from Will Smeed, although England pair Ben Duckett and Jacob Bethell were dismissed for single figures as their quiet tournaments continued.
They had been put under pressure after Behrendorff conceded 14 runs from his 15 balls, the only bowler in the match to concede less than a run a ball.
The Invincibles, who lost for the first time this year after two successive wins, recovered from 5-114 from 73 balls to get to 8-180 thanks to Donovan Ferreira's 63 off 29 deliveries.
