Second seed Murray shook off his post-Wimbledon cobwebs with a fighting 6-4, 7-6 (7/2) victory over Marcel Granollers.
The win — his 13th in succession — came just over a month after the Scot made history with the first British Wimbledon men's singles title since 1936.
French Open champion Nadal, seeded fourth, showed no mercy to Canada's Jesse Levine in a 6-2, 6-0 win as the Spaniard returned to action for the first time since his shock Wimbledon opening round loss to Steve Darcis six weeks ago.
Nadal saved three break points while breaking Levine five times in 71 minutes on court.
“The knee is not bothering me much,” said Nadal. “In the last couple of days, I was able to practice with no limitation, that is the most important thing.”