The 24-year-old, ranked 114th in the world, came through qualifying before the tournament and is only making her third appearance in a Grand Slam main draw.
She previously reached the second round at Wimbledon in 2022 and lost in the first round at the Australian Open in 2025.
Chwalińska made an uncertain start, dropping the first set and committing 14 unforced errors.
She grew steadily into the match, however, mixing deep groundstrokes, drop shots and lobs to unsettle Sakkari.
The Greek player, ranked 49th and a former world number three, committed 36 unforced errors across the second and third sets – against Chwalińska's 14 – as her frustration visibly increased as the match wore on.
A pivotal moment came in the third set when Sakkari held three break points at 40-0 on the Pole's serve, only for Chwalińska to win five consecutive points and move 3-1 ahead.
Chwalińska has already secured a place inside the world's top 100 for the first time, with a virtual ranking of 75th.
She will face France's Diane Parry, ranked 92nd, in the fourth round on Monday.
(ał)
Source: PAP