Evans defeated Karen Khachanov of Russia on Tuesday in the longest match in US Open history, lasting five hours and thirty-five minutes.
48 hours later, the 34-year-old defeated world number 36 Navone 6-4 6-3 6-3 in a more convincing match to go to the third round.
The top-seeded British woman, Katie Boulter, lost to Jessica Bouzas Maneiro in a “horrendous” match earlier on Thursday, while Jack Draper defeated Argentina’s Facundo Diaz Acosta with ease.
Despite having a great start in the first set, Boulter, the 31st seed, lost 7-5 7-5 to Spain’s 74th-ranked Bouzas Maneiro.
With a 6-4 6-2 6-2 victory, British men’s number one Draper advanced to the third round with ease.
Botic van de Zandschulp, who upset Carlos Alcaraz, the third seed and title candidate, will be his opponent.
Evans has lost two straight matches on the ATP Tour this year before defeating Navone.
After falling behind 3-0 in the opening set, the world number 184 rallied to win six of the next seven games to seize the initiative.
He held off Navone’s late charge in the third set, overturning an early lead and breaking twice more before.
After two hours, Evans and the supporters celebrated when his opponent made a long forehand on the second match point.