The four-time Grand Slam champion, who has reached 14 successive major quarter-finals, won 6-1, 7-6 (11/9) on Court One to secure a last-32 meeting with former French Open winner Jelena Ostapenko.
"That was a true battle and I'm super happy that I was able to stay in that second set to get into that tie-break," said Sabalenka.
"She really tested me and I'm super happy to pass the test."
Sabalenka has never won Wimbledon, losing in the semi-finals on each of her past three visits.
Kessler missed two set points when serving for the second set at 5-3 ahead, before Sabalenka fought back and took a tie-break, in which her 57th-ranked opponent saw another two set points come and go.
