World number two Djokovic beat Italian Andreas Seppi 7-6, 6-2 while Olympic gold medallist Murray came past American Sam Querrey 6-2, 6-4.
Serb Djokovic, who won the ATP Masters tournament at Toronto last week, knew he was in for a tough test from Seppi after needing to come back from two sets down to win in five when they met in the French Open.
It was a tight affair in the first set, won on a tie-break by Djokovic, and then the five-times grand slam singles champion comfortably secured the second.
“I wasn’t satisfied with my performance, I will have to play much better than this in order to go far,” said the 25-year-old Djokovic.
“There were a lot of unforced errors from both of us. It wasn’t a really pretty match.”
Murray pulled out of Toronto last week due to concerns over his knee but he looked in good shape as he dominated Querrey.
The Scotsman’s serve was too much for his opponent and his defence was strong enough to break serve on three straight service games in the first set to get in control.
There was better news for another American, Mardy Fish, who beat Argentine Carlos Berlocq 6-3, 6-1.
But James Blake made an early exit after 22-year-old Japanese Kei Nishikori recovered from a poor first set to beat the American 2-6 6-4, 6-4.
German Tommy Haas and Australian Lleyton Hewitt have both hinted at mini-revivals in form but their bids here ended in the second round.
Haas battled hard in the first against sixth-seeded Argentine Juan del Potro but ended up losing 7-5, 6-2 and Hewitt was badly out of sorts as he was crushed 6-2, 6-0 by Serb Viktor Troicki.
Swiss world number one Roger Federer is in action later on Wednesday against Russian-American Alex Bogomolov Jr.