The top seed was followed into the winners' circle by a restrained Andy Roddick, who let his tennis do all the talking in a brutal 6-1, 6-3, 6-3 demolition of Brazilian Flavio Saretta.
In the women's draw, fifth seed Amelie Mauresmo of France overpowered Thai Tamarine Tanasugarn 6-2, 6-2 to reach the quarter-finals.
Mauresmo will next face world number one Kim Clijsters of Belgium or 17th seed Meghann Shaughnessy of the U.S., who face off in a night match.
Earlier, third seed Lindsay Davenport became the first woman through to the quarters when she struggled past Russian Nadia Petrova 6-0, 6-7, 6-2.
Davenport, the 1998 U.S. Open champion, had a pain-killing injection in her toe before the season's last grand slam, and she appeared to be moving gingerly towards the end of the one hour 52 minutes match.
"It is what it is," Davenport told reporters of the injury. "I still feel pretty good...was able to get through it."
Davenport next meets Paola Suarez, the 24th seed from Argentina, who beat Russian Elena Likhovtseva 6-2, 3-6, 7-5.
Having been accused by Croatia's Ivan Ljubicic of influencing linesmen with his animated behaviour in an emotionally-charged second-round clash, Roddick was subdued throughout his 87-minute match.
DESERVED FAVOURITE
His tennis certainly did not suffer, however, and he heads into the next match against Belgian Xavier Malisse or Russian qualifier Dmitry Tursunov a deserved favourite to win his first Grand Slam.
"I didn't need it," he said, explaining why he had been subdued. "Just so happened that the other night I really needed it," he added, referring to his on-court antics of pumping himself up.
World number one Agassi barely put a foot wrong once his match, held over from Saturday night, resumed under cloudless skies with the American leading 6-3, 0-1.
"I think a lot of things went well. I managed to sneak out that second set tiebreak and then I was off to the races," Agassi smiled.
"It was a tough day yesterday for both me and the Y-man," he added, referring to the rain that had halted the match overnight.
Twice a winner at Flushing Meadows and three-times runner- up, including last year, the 33-year-old Agassi underlined his determination to win a ninth grand slam with a top-notch performance.
His receiving radar will have to be fully functional in the next round, however, when he lines up opposite massive server Taylor Dent of the U.S.
Earlier, 22nd seed Younes El Aynaoui thrilled a Grandstand Court crowd with a pulsating 7-6, 5-7, 3-6, 6-3, 7-6 win over 10th-seeded Czech Jiri Novak.
The delighted Moroccan ripped off his shirt and hurled his rackets into the crowd after clinching victory. El Aynaoui meets Spain's Carlos Moya in the fourth round.
"When I was watching tennis I would love to get a piece of a tennis player, a wristband or anything," El Aynaoui said.
"So I am always trying to give things away and make people happy...I'm trying to get some more rackets right now."
