The 29-year-old Czech fighter was behind on two of the judges' scorecards heading into round five when he produced a rear-naked choke submission with just 28 seconds left on the clock to inflict a heartbreaking defeat on 42-year-old Teixeira.
The breathless Singapore clash will be remembered as a classic given the nature of number two ranked Prochazka's stunning late comeback to dethrone Teixeira and earned 'Fight of the Night' honours.
The win also means Prochazka is the first Czech Republic fighter to wear the belt.
He has now won 29 off his 33 professional fights - 25 of those by knockout and three by submission.
"It's amazing and I'm glad. It was a true war. Glover is a true warrior," Prochazka told BT Sport.
Brazil veteran Teixeira took his European challenger down twice in the opening round and survived some scares of his own in a see-saw encounter but looked to be on the brink of victory.
A brutal fourth round saw both men unleash heavy blows and Teixeira appeared to be edging ahead after a flurry of savage hits on Prochazka in the fifth.
He tried to take the fight to the floor but it proved a costly mistake as Prochazka somehow reversed position and locked in a choke forcing Teixeira to tap out.
Teixeira, who became the oldest fighter to win a UFC title when he beat Jan Blachowicz in October last year, was running on empty when he surrendered the bout but had no complaints with his devastating loss.
He said: "He (Prochazka) is a very skilled guy on the ground.
"I gave my all out there, there are no excuses."