She will face Sofia Kenin in the last four.
Filed: Saturday, September 15, 2018 at 15:00 UK
Last Updated: Saturday, September 15, 2018 at 15:00 UK
The world number 227 produced a confident display, winning 85% of her first serve points to topple her Croatian opponent 6-3 7-5 and book her place in the semi-finals.
Pegula needed just one break of serve off the back of a double fault from Martic to close out the opening set, while the second set saw the pair exchange breaks.
With the scores tied at 5-5, the American played aggressively to go 6-5 up before holding her nerve to serve out the match.
She will now face a meeting with compatriot Sofia Kenin, who reached the second WTA semi-final of her career by ousting number three seed Monica Puig.
The 19-year-old hit six aces and lost just six points on serve as she dismissed the Puerto Rican 6-3 6-1 in 55 minutes.
As the number five seed, Kenin is now the highest-ranked player left in the draw in Quebec.
British number three Heather Watson sealed her spot in the final four with a straight-sets win over Canada’s Rebecca Marino.
Watson took two breaks – losing her own serve once – to take a one-set lead, before needing just one break in the second to clinch the match 6-3 6-4.
Up next for the Briton is Pauline Parmentier, who beat American Varvara Lepchenko 7-6 (7/5) 6-1.
At the Japan Women’s Open, top seed Zhang Shuai overcame injury and weather delays to reach the semi-finals with victory over defending champion Zarina Diyas.
The 29-year-old was carrying a leg injury but it did not prevent Zhang securing a 6-4 7-5 win to advance to the last four.
American qualifier Amanda Anisimova will face Zhang for a place in the final after 17-year-old secured her maiden WTA semi-final appearance at the expense of Anna Schmiedlova.
A near-three hour rain delay was not enough to knock Anisimova off her stride as she eased to a 6-3 6-1 win.
Number four seed Wang Qiang assured herself of a spot in the other semi-final as she recovered from a slow start to see off Madga Linette of Poland.
Linette took the first two games before Wang hit back by taking the next eight on her way to a 6-2 6-2 success.
The final quarter-final of the competition will be completed on Saturday after Ajla Tomljanovic’s meeting with Hsieh Su-Wei was postponed with less than three minutes played.
A heavy downpour caused the match to be halted inside the first game with the Taiwanese player leading 30-15 on her serve.
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