The Canadian will meet another unseeded American, Donald Young, in a Saturday semi-final after Young upset seventh-seeded South African Kevin Anderson 3-6 7-6(3) 6-2.
The other semi-final on the hardcourt at the William H.G. Fitzgerald Tennis Center will pit sixth seed Richard Gasquet of France against either Colombia's Santiago Giraldo or Canadian Vasek Pospisil.
Giraldo and Pospisil had completed just two points in their decisive third set on Friday before the match was suspended because of rain. They are scheduled to resume on Saturday before the winner takes on Gasquet later in the day.
Gasquet had the easiest quarter-final match on Friday, waltzing past Japan's Kei Nishikori 6-1 6-4 in less than an hour.
Nishikori, the fourth seed, appeared hampered by an ankle injury that restricted his mobility as the Frenchman rode a strong backhand to improve his career head-to-head record to 5-0.
"I saw he had a little problem," Gasquet told ESPN.
STERNER TEST
Raonic had a much sterner test against Johnson, who beat two other big men, American John Isner and Croat Ivo Karlovic, to reach the last eight.
Up against another powerful server, Johnson looked the more impressive in the first set, holding serve with ease.
But neither player could prise out so much as a break point and once Raonic won the tiebreak 7-2, he dominated the second set, twice breaking Johnson to close the match out in just under 80 minutes.
"It's tough after a few weeks off but I'm happy with the way things are going," said Raonic, who got within one match of the Wimbledon final before losing to Roger Federer.
"My attitude and mentality have been getting me through a lot of important stages."
Left-hander Young battled for over two hours before outlasting Anderson in a match in which the second set tiebreak proved crucial.
Both players broke serve twice, and Young did it at the right times to move within sight of what would be just his second ATP World Tour final.
In the women's semi-finals, second seed Ekaterina Makarova will meet sixth seed Svetlana Kuznetsova in an all-Russian encounter while New Zealand's Marina Erakovic will face Japan's Kurumi Nara.
(Reporting by Andrew Both in Cary, North Carolina)
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