The Scot looked laboured at times during his quarter-final victory over Bernard Tomic in Cincinnati, but 10 aces proved too hot to handle for the Australian in a 6-4, 6-4 loss.
Next up for the Olympic champion – now on a run of 21 straight wins – is Canada’s Raonic, who was on the losing side when Murray won his second Wimbledon title in July.
On the other half of the draw are world No 14 Marin Cilic and the unseeded Grigor Dimitrov who will meet in the other semi-final.
Bulgaria’s Dimitrov dominated American No 1 Steve Johnson on his way to claiming a 7-6 (10/8), 6-2 triumph.
Cilic benefited from fellow Croatian Borna Coric’s retirement with the scoreline reading 6-2, 0-0.