Nadal, a beaten finalist to Stan Wawrinka last year, turfed out Russian journeyman Mikhail Youzhny in an uncomplicated straight sets victory, while Murray began a campaign hoping to end the heartbreak of three runners-up finishes in Melbourne.
The two-time Grand Slam champion Scot emerged a 6-3, 6-4, 7-6 (7/3) winner over India's Yuki Bhambri on Margaret Court Arena.
Rising Bulgarian star Grigor Dimitrov also swept to victory over Germany's Dustin Brown in just 69 minutes, while Czech seventh seed Tomas Berdych blew away Alejandro Falla.
Spanish world number three Nadal was delighted with his straight forward win over Youzhny, a former US Open semi-finalist, and will next play American qualifier Tim Smyczek.
"Very positive result for me. I think a very good start. Very important," Nadal said.
Youzhny was considered a testing first-up opponent as the Spaniard searches for matches to work his way into the men's draw.
But the third seed only conceded one break point on his serve, while claiming six service breaks on the Russian in a convincing win.
His lack of match fitness was apparent in Qatar this month when he was humiliated in the first round by German Michael Berrer, a qualifier ranked outside the top 100.
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