Canadian second seed Raonic fired 16 aces and lost only nine service points in defeating American Steve Johnson 7-6 (7/2), 6-2, taking only 79 minutes to book his third semi-final of the season.
"I'm getting better and better," Raonic said. "I played the right way at the end of the sets. When I got the advantage I kept the intensity.
"I've gotten better at knowing what I need to do. I step up in the tie-breakers and that has worked out well."
Raonic, seeking his sixth ATP title, lost the Rome semi-final to top-ranked Novak Djokovic and at Wimbledon to 17-time Grand Slam winner Roger Federer.
Next up for Raonic is a first career meeting with 25-year-old US left-hander Donald Young, who outlasted South African seventh seed Kevin Anderson 3-6, 7-6 (7/3), 6-2, to extend his best run in three years.
"He's very talented and he's very dangerous," Raonic said. "He neutralizes well. He defends well."
French sixth seed Gasquet ripped Japanese fourth seed Kei Nishikori 6-1, 6-4 in only 59 minutes to reach the other semi-final, but he must wait until Saturday to learn his opponent.
Giraldo won the first set 7-6 (7/4) while Pospisil took the second set 6-3 and the first two points of the third set on his serve before play was halted.
Gasquet is 2-0 vs Giraldo, winning at Lyon in 2008 and in a 2011 Wimbledon opener, but lost his only match against Pospisil last year at Shanghai.
Gasquet, who improved to 5-0 against Nishikori, withdrew from Atlanta last week with a sore right arm, but fired nine aces and won all three break-point chances he created against 11th-ranked Nishikori.
"It's a big victory for me to win against him," Gasquet said.
Gasquet, nagged by a back injury earlier this season, reached his fourth semi-final of the year in quest of his 11th career title and first since last October at Moscow.
"I was stopped for about three months," Gasquet said. "It's difficult. The level is very high and you have lost your confidence. It's very important to keep your belief."
Nishikori connected on 62 percent of his first serves to 58 percent for Gasquet, but the Frenchman won 85 percent of his first-serve points to 64 percent for Nishikori.
- Disappointed Nishikori -
"This is very disappointing," Nishikori said. "Didn't do anything. I could do better. Hopefully I'll play better next week."
Young's Washington run is his deepest since reaching his only ATP final in 2011 at Bangkok, where he lost to Britain's Andy Murray.
"I'm just believing a little more. I'm staying in the matches more, not tapping out," Young said. "I'm still fighting and able to hang in there."
On the women's side, Russian sixth seed Svetlana Kuznetsova, the 2004 US Open and 2009 French Open champion, won by walkover when American Vania King withdrew with a right hip injury.
Kuznetsova, who made her first WTA final since 2011 just four months ago at Oeiras, has a semi-final date with Russian second seed Ekaterina Makarova, who ousted fifth-seeded compatriot Anastasia Pavlyuchenkova 7-6 (7/3), 6-3.
Japan's Kurumi Nara defeated France's Kristina Mladenovic 6-3, 6-1 to reach a semi-final against New Zealand's Marina Erakovic, who beat Serbian Bojana Jovanovski 6-4, 6-4.