Pegula, a 2024 champion on the Berlin grass, won 7-6(5), 7-6(8) in sweltering conditions in the German capital.
In their first meeting since Pegula ended Keys' title defence at the Australian Open in January, both players each broke serve once in the opening set and forced a tiebreak, which Pegula won.
Pegula ran out to a 4-2 lead in the second, but Keys fought back to once again set up a tiebreak. Pegula triumphed 10-8 in the tiebreak to extend her winning run to seven without defeat over fellow Americans this calendar year.
The 32-year-old American will face either world number one Aryna Sabalenka or Nikola Bartunkova in the semi-finals on Saturday.
Eighth seed Linda Noskova defeated Spanish wildcard Paula Badosa 6-1, 6-3 in Friday's second quarter-final.
Later on Friday, world number eight Elina Svitolina takes on Alexandra Eala, who eliminated Elena Rybakina on Thursday.
