Serbian top seed Djokovic battled to a 6-2 6-7 (4-7) 7-6 (7-2) win over exciting Frenchman Gael Monfils in Toronto.
In his first match since winning Wimbledon, the three-time Rogers Cup champion was a break down in the deciding set before fighting back.
Monfils was two points away from a first win in 10 meetings against Djokovic, who faces another Frenchman in the third round.
Jo-Wilfried Tsonga, the 13th seed, meets Djokovic after a 7-6 (8-6) 6-4 victory over countryman Jeremy Chardy.
Murray, also in his first outing since Wimbledon, took just 54 minutes to dispose of Australian wildcard Nick Kyrgios 6-2 6-2.
Murray, the British eighth seed, only lost six points on serve in a dominant performance against the exciting Kyrgios.
Awaiting Murray is Frenchman Richard Gasquet after the 12th seed overcame Croatian Ivo Karlovic, who served 27 aces in the 5-7 7-6 (7-5) 6-3 loss.
It was a good day for the seeds at the ATP 1000, hard-court event.
Fresh from his Washington title win, local favourite and sixth seed Milos Raonic battled to a 4-6 7-6 (7-2) 7-6 (7-4) win over American wildcard Jack Sock.
Grigor Dimitrov, the Bulgarian seventh seed, overcame a slow start to beat American left-hander Donald Young 4-6 6-2 6-3.
Czech fourth seed Tomas Berdych fought past Chinese Taipei's Lu Yen-Hsun 6-7 (4-7) 6-4 6-4 in two hours and 18 minutes.
Croatian 15th seed Marin Cilic edged past Tunisian lucky loser Malek Jaziri 4-6 6-0 7-6 (7-4) and Spanish fifth seed David Ferrer was a 6-4 2-6 6-1 winner against American veteran Michael Russell.
Spanish 17th seed Tommy Robredo completed a 7-5 6-4 win over France's Gilles Simon.
Ernests Gulbis and Fabio Fognini were the only seeds to fall.
Frenchman Julien Benneteau upset Latvian Gulbis 7-6 (7-4) 6-3 and Fognini was beaten by South African Kevin Anderson 7-5 6-2.
Croatian veteran Ivan Dodig beat Italian Andreas Seppi 6-4 3-6 7-6 (7-5) and Spain's Feliciano Lopez was too good for American qualifier Tim Smyczek 7-5 6-4.