The 19-time Grand Slam victor Federer is seeking his 27th Masters 1000 title and his third Canadian Masters crown after wins in 2004 and 2006.
Shapovalov will now be ranked 67th in the world when the new list comes out.
Federer, was never seriously pushed by the Spaniard as the Swiss maestro secured the first break in the 9th game of the opening set. He is 26 times a champion at this level, whilst Haase is competing in his first Masters 1000 semifinal.
Flag-waving fans in the packed grandstands at Uniprix Stadium were hoping for more magic, but the German was too strong, winning 81 per cent of the points off his serve compared to 64 per cent for Shapovalov. Rafael Nadal would be playing his third round match at the Rogers Cup against former French Open quarter-finalist Igor Andreev who had previously beaten Tomas Berdych in the second round.
Shapovalov's dream run will now be put to the test by Alexander Zverev, who defeated Kevin Anderson for the second time in a week following their meeting in last Sunday's Citi Open final. I don't know how much Rafa cares about the year-end number one or if he just cares about getting back to it for a short while. I know that's not going to be the problem for me. He recovered from the precipice, winning a mammoth rally at 15-40 with his physical superiority, and eventually went on to claim a break for 6-5 when Shapovalov-for the third time in the evening-double-faulted a break away.
Federer's 93 titles and 1114 wins also dwarf Haase's 2 titles and 186 wins.
"Worst loss of the year because I lost against a player with a lower ranking", Nadal said.
Any misgivings Roger Federer may have had about playing in the Rogers Cup are behind him now that the Swiss master has reached the final.
With top seed Rafael Nadal knocked out in the third round by Canadian teenager Denis Shapovalov, 19-time grand slam victor Federer is thick in the fight for a return to the top of the ATP list.
Caroline Wozniacki defeated World No. 1 Karolina Pliskova 7-5, 6-7 (3), 6-4 in a marathon Rogers Cup quarter-finals match in Toronto marred by four rain delays on Friday.
Polansky earned a stay of execution after holding serve in the sixth game to make it 5-1, but Federer raced into the next round with a comfortable hold, finishing with an emphatic overhead smash. "I still have to work really hard every day". I started to believe more and more again. His quarterfinal opponent was Diego Schwartzman, who had upset 3rd seed Dominic Thiem earlier in the week.
The win was an encouraging step forward for Stephens, who missed 11 months due to a foot injury and stumbled to a first-round defeat at Wimbledon against Alison Riske in her return to the court. "Today, I felt that I didn't get into the rhythm of the match and I didn't feel the ball well".