The 10-times grand slam winner, who is battling a niggling shoulder injury and has said his knees were still a concern, took 44 minutes to take the first set against the persistent American.
The 25-year-old left-hander ran away with the next two sets, however, dominating from the baseline and giving Kuznetsov just two break point opportunities when he was serving for the match before clinching victory in 106 minutes with his ninth ace.
Nadal will now meet Tommy Haas in the second round after the German veteran beat American qualifier Denis Kudla 7-6 3-6 6-0 7-5.
Image: Spain's Rafael Nadal waves to the crowd following his first round match against Alex Kuznetsov of the US at the Australian Open tennis championship, in Melbourne, Australia, Monday, Jan. 16, 2012.
Text: Reuters/PTI Images: AP