The big-serving Kyrgios struck 30 aces and won the final nine points of the match to end the punishing affair under the lights at Louis Armstrong Stadium.
"His level today was incredible, I was not expecting an absolute war," Kyrgios said in an on-court interview.
"That could have gone either way. He was up a break early in the fourth but I played some really risky tennis late in the fourth set to win. I'm just happy to get through."
In their first career meeting, Kyrgios unleashed some spectacular shotmaking in the tiebreak and rode an early break in the second set to take a 2-0 lead.
Bonzi responded by taking the third set and a decider appeared all but inevitable when Kyrgios trailed Love-40 while serving at 4-4 in the fourth.
"My mentality was I'm probably going to get broken. I was almost gearing myself up for a fifth set," Kyrgios told reporters.
"In those moments I just played really low percentage. I just kind of hit a dropshot here, hit the forehand cross-court, faked him out with the underarm... it got me out of jail."
After serving his way out of trouble he sealed the match by breaking serve for a fourth time when Bonzi, who made some acrobatic dives for balls during the match, was unable to will his shot over the net on match point.
The Kyrgios win sets up a third-round meeting with American JJ Wolf (23), who got past Alejandro Tabilo (25) 4-6 7-5 6-4 6-3 earlier in the day, and keeps alive the potential for a showdown with world number one and defending champion Daniil Medvedev (26) in the fourth round.
Kyrgios not high on the smell of cannabis at US Open
Nick Kyrgios said the odor of cannabis that permeated Louis Armstrong Stadium during his second-round match at the US Open killed his buzz and left him fearing that it could aggravate his asthma.
Kyrgios took time during the second set of his win over Bonzi to complain to the chair umpire about the smell, which led to a warning to the crowd to "refrain from smoking." Smoking is not permitted on the tournament grounds.
The outspoken Australian told reporters after the match that it was no laughing matter.
"People don't know I'm a heavy asthmatic," Kyrgios said after his victory over the Frenchman.
"When I'm running side to side, I'm struggling to breathe, probably not something I want to be breathing in between points."
Kyrgios acknowledged that the loud, raucous atmosphere at the US Open sets it apart from the three other Grand Slam tournaments.
"The US Open, it's a very different vibe to everywhere else," he said.
"I feel like Wimbledon was so proper. Australian Open, you kind of expect it there, being an Aussie.
"But here, it's just like noisy. Point in, point out, I can't barely hear. Half the time, I can't even hear my team because it's so noisy all the time."
