Djokovic, who was among several players playing two matches to make up for Thursday's washout, defeated German Tommy Haas 6-3 3-6 6-3 hours after dispatching American Sam Querrey 6-4 6-4 in a contest interrupted by a three-hour rain delay.
The top-seeded Serbian, who needed two and a half hours to get by Haas, will next face fifth-seeded compatriot Janko Tipsarevic, who kicked off the evening session with a 6-4 6-4 win over Spain's Marcel Granollers.
Tipsarevic had reached the last eight by beating Croatia's Marin Cilic 6-2 6-4 earlier on Friday.
Raonic, playing in his home tournament for the first time since breaking into the world's top 25, fell 7-6 6-4 to eighth-seed American John Isner, who earlier edged Germany's Philipp Kohlschreiber.
The big-serving Canadian was on court for the first time since Tuesday, having been handed a walkover to the quarter-finals after Olympic singles champion Andy Murray pulled out due to injury.
While Raonic managed 13 aces in the match, Isner controlled the rallies, clinching the match with a volley to the open court after one of his own booming serves left the 16th seed well out of position.
Isner will now face Frenchman Richard Gasquet, a 5-7 6-1 6-1 winner over American Mardy Fish.
- Marcel Granollers
- Janko Tipsarevic