After conquering top seed Daniil Medvedev, former world number three Dimitrov recovered from a set down to upstage eighth seed Hurkacz on Friday (AEDT).
Norrie shocked 11th seed Diego Schwartzman in straight sets at the ATP 1000 tournament.
Bulgarian star and 23rd seed Dimitrov reached his first ATP Masters 1000 semi-final of the season with a 3-6 6-4 7-6 (7-2).
Dimitrov showed he is the comeback king once again, having also saved two break points at 3-3 in the second set.
A semi-finalist at the US Open (2019), Australian Open (2017) and Wimbledon (2014), Dimitrov then squandered a 5-2 lead in the deciding set before eventually prevailing in a tie-break for his 100th Masters 1000 victory.
NORRIE BOOSTS TURIN BID
Norrie's hopes of qualifying for the ATP Finals in Turin received a boost after breezing past Schwartzman 6-0 6-2.
Amid a career-best season, Norrie advanced to his maiden ATP Masters 1000 semi-final, with the 26-year-old to replace Daniel Evans as the new British men's number one.
Seeded 21st, Norrie – who has 45 Tour-level wins in 2021 – now has next month's Finals firmly in sight, having started the day 945 points behind ninth-placed Hurkacz in the race to Turin.
"I have been pretty consistent this year," Norrie said after 74 minutes on court. "I think I am really doing the fundamentals well on serve and return and playing the big points better.
"I have been a little more aggressive and feel I am learning more as I go along and becoming more experienced. We are really happy."