Bartunkova has had a breakthrough year, beating then world number 10 Belinda Bencic at the Australian Open and finishing runner-up at the grass court event in Birmingham earlier in June.
Her flat strokes and booming return of serve confounded Sabalenka, who quickly found herself 5-1 down.
Having lost four games in a row, Sabalenka saved four set points on her serve and had two break-back points as Bartunkova tried to close out the opener – only for the 20-year-old to fire two huge first serves beyond her.
The world number 62 let out a huge scream of celebration as she took the lead, and her positive play allowed her to take the first four games of the second set.
Sabalenka’s serve had barely been a factor – one hit the frame of the racquet and sailed out of court at one point – until she held to love to get on the board.
Although she had to save another break point, Sabalenka won the next five games to get in front for the first time in the match before taking the tie-break.
Momentum swung in the final set, with Sabalenka twice being wrestled back from a break up, but a huge forehand winner set her up to serve for the match at 5-4.
Two match points came and went before a trademark forehand cross-court secured victory for the top seed.
While the gritty victory will please Sabalenka, she was also icing her right shoulder at the changeovers – an injury that ruled her out of Wimbledon two years ago.
Elsewhere, world number two and 2022 Wimbledon champion Elena Rybakina withdrew from the Bad Homburg Open with a hip issue.
