Hussey was playing in his first ATP Tour match, having been called up to replace Japan’s Kei Nishikori at very late notice.
He needed just 64 minutes to complete victory over Navone, who lost to Jack Draper in the first round at Queen’s last week.
“I’m shaking, I don’t know if you can tell,” Hussey, 27, said.
“I just came out here and wanted to enjoy it. I was sat there 45 minutes before the match and didn’t know I was going to play today.
“I really didn’t know much about Mariano but I knew that he’s played predominantly on clay so I thought if I could come out here and just swing and go for my shots and try and rush him that that could be the best plan and, luckily, it all came off.”
Meanwhile, British number five and wildcard Liam Broady fell to a 6-3 6-3 loss against Japanese qualifier Yoshihito Nishioka on his return from injury.
Broady injured his ankle in March and had his return to competition delayed after sustaining a concussion when he hit his head on a car boot earlier this month.
