Tsitsipas saved two match points in a 3-6, 7-6 (11), 6-4 victory over second-seeded defending champion Alexander Zverev, and the top-seeded Nadal beat sixth-seed Marin Cilic 2-6, 6-4, 6-4.
Tsitsipas, who will turn 20 on Sunday, will next play the victor of the evening semifinal between top-ranked Rafael Nadal of Spain and Russia's Karen Khachanov.
'It's been nearly 10 years (2010) since I last played in Toronto, ' Nadal said of the event which comes to the city in even-number years as it trades with Montreal. Obviously when I played Washington, slightly slower, also played a couple of matches in the evening there, was quite slow, whereas here obviously quite lively.
Anderson's sweep past reigning ATP World Tour Finals champion Dimitrov was a rematch of their 2014 quarter-final duel in Canada when Dimitrov claimed one of his six wins against the South African. "I felt I played really well right from the beginning", Anderson said. "It's been the key factor", Tsitsipas said on Saturday.
The 20-time major victor skipped Toronto last week to pace himself with the tournament at Flushing Meadows followed by the Laver Cup in Chicago in mid-September. For me just having this trophy with me means a lot.More news: Turkey takes action in bid to curb currency crisis
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"Playing in a Masters 1000 final is the best thing that can happen on your birthday".
"He was normal like all of us and he managed to become this beast, this monster that he is today", Tsitsipas said.
But Federer believes the time off and his need to preserve his body - he played just 57 matches previous year compared to 97 at his peak - has given him a simpler path, mentally as well as physically.
"Every time I play her, she makes me a better player, she makes me raise my level".
I don't like to miss events.
The 32-year-old Spaniard was the biggest name set to take part in the tournament. After that I accepted the situation, just fought back and tried to stay positive.