Federer delayed his opening match at the Australian Open warmup until the fifth day because of a flu-like illness and was playing Dimitrov in the quarterfinals on less than 24 hours rest.
His serve in the first set was almost flawless, dropping just two points, and he appeared to be on course with break-point chances for another straight-set victory over the young Bulgarian sometimes likened to him because of their similar styles before Dimitrov rallied.
Federer, after showing signs of fatigue in the second set, took a quick break before the third, and then went on a roll to set up three match points in the ninth game. Again Dimitrov rallied, winning five consecutive points and forcing Federer to serve it out which the 17-time major winner duly did.
By holding off Dimitrov, who is 10 years his junior, Federer set up a meeting with 22-year-old Dominic Thiem, the youngest player in the top 20.
Tomic ended Kei Nishikori's streak of semifinal appearances at the Brisbane International with a 6-3 1-6 6-3 win, his first over a top 10 player on home soil.
After an exchange of breaks early in the third, Tomic
clinched it on his first match point, avenging a loss to Nishikori last year.
"That was very, very special to me," Tomic said. "Last year, unfortunately, I lost very comfortably to Kei, and today played very different."
Raonic relied on his big serve to dictate a 6-4 6-4 win over world No 78-ranked Lucas Pouille.
Two-time Australian Open champion Victoria Azarenka and US qualifier Samantha Crawford played the other semifinal match.
In Auckland, Julia Goerges reached her sixth WTA final and her first in four years when she beat qualifier Tamira Paszek 6-4 6-2 in the ASB Classic semifinals.
Goerges, ranked 50th, last reached a final in Dubai in 2012 when her ranking peaked at world No 15.
Sloane Stephens was leading 5-2 in the first set of the other semifinal match against third-seeded Caroline Wozniacki when rain halted play, forcing it to be postponed to Saturday.
The Australia Green team can seal a spot in the final against Ukraine with a win over France late Friday, and Nick Kyrgios gave the home team a 1-0 lead when he beat Kenny De Schepper 6-4, 6-4.
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