Bejlek broke the Belarusian three times in the second set, rallying from 4-1 down and securing the win with a love game capped by an ace.
“I lost my words — it feels incredible,” Bejlek said after her first win over a top-10 player.
“I was playing what I was feeling and not really thinking. I was trying not to be nervous and just play. I believed in myself no matter what.”
Bejlek, who won the Abu Dhabi hard court title in February as a qualifier, booked a quarterfinal clash with American Madison Keys.
It was yet another setback for Sabalenka as the start of the US Open looms on 30 August.
The four-time Grand Slam champion was ousted in the fourth round of the Toronto Masters last week, having lost in the same round at Wimbledon and in the quarterfinals at Roland Garros.
Zverev’s match was interrupted by rain for 90 minutes in the seventh game of the second set and had two more five-minute pauses as drops were dried from the court.
French Open champion Zverev had a chance to close it out at 6-5 in the second-set tiebreaker but stuffed a volley into the net.
The German again gained an edge in the deciding set with a break for 4-2, but Paul broke back in the next game and again for a 5-4 lead on the way to his third win over Zverev in their Last Four meetings.
“I’m not sure how I did it,” Paul said.
“I put some returns in, he gave me some looks at second serves and he threw in a few doubles (faults). That always helps a ton. I went after the ball a bit more, I was having fun out there.”
Second seed Felix Auger-Aliassime of Canada was another casualty, falling 6-3, 6-4 to American Frances Tiafoe.
Zverev’s conqueror Paul next faces Roland Garros runner-up Flavio Cobolli, who labored two and a half hours to engineer a turnaround against red-hot Spaniard Rafael Jodar 4-6, 7-6 (7/3), 6-3.
American sixth seed Taylor Fritz dispatched Australian Chris O’Connell 6-4, 6-3.