The world number two won 6-2 6-0 in 66 minutes and will next play Rafael Nadal, who beat Stan Wawrinka 6-1 6-4.
It was a much improved performance from Murray, who broke 10th seed Raonic's serve five times.
Jo-Wilfried Tsonga beat Roger Federer 6-3 2-6 7-5, and fellow Frenchman Gael Monfils beat Marcel Granollers 6-2 6-4.
"It's the most challenging surface for me every year," said Murray.
"It normally takes me a few weeks to remember what I need to do, how to move, the way to build up the points and making sure you don't rush."
Murray needed almost three hours to beat Benoit Paire on Thursday and had struggled for form since the Australian Open in January - but he was close to his best against Raonic.
The Scot, 28, dominated all aspects of the game but was especially aggressive on the return, denying the big-serving Raonic a single ace and breaking five times.
"The two most important shots in tennis I did really well," added Murray.
"I was getting a good read on the serve and, when he missed the first serve, I was being very offensive on the second serve return and putting him under pressure.
"The serve and the return for me were the best they've been for a while and I'm glad, because they weren't so strong the last couple of matches."
Jamie Murray boosted his hopes of hanging on to the doubles world number one spot for a while longer as he and Brazil's Bruno Soares reached the semi-finals.
The pair beat sixth seeds Rohan Bopanna and Florin Mergea 6-2 6-3, despite Murray requiring treatment on his thigh at one stage.
Murray leads Marcelo Melo by just five points in the rankings and will face the Brazilian, and partner Ivan Dodig of Croatia, in the last four on Saturday.
Andy Murray and Dom Inglot had a match point but could not convert as they lost 6-4 3-6 12-10 to France's in-form Nicolas Mahut and Pierre-Hugues.
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Britain's Andy Murray is through to the Monte Carlo Masters semi-finals following an impressive win over Canadian Milos Raonic.