Radwanska, who had been extended to three sets in three of her four matches against 25th seed Garcia, romped into the round of 16 with a 6-2 6-3 victory in breezy conditions at Louis Armstrong Stadium.
It will be the 27-year-old Radwanska's fifth trip to the fourth round at the U.S. Open but she has failed to advance beyond that stage in New York, unlike the other grand slams.
Radwanska was runner-up to Serena Williams at Wimbledon in 2012, becoming the first grand slam finalist from Poland in the Open era. She is a twice semi-finalist at the Australian Open and has reached the quarter-finals at Roland Garros.
"That means everything," Radwanska said on court about her goal to go deeper into the year's last grand slam championship.
"I hope I can play even better than today in the next round and reach my first quarter-final here."
Radwanska, who won her 19th career WTA title last week in the New Haven warm-up event for the Open, gave herself a high grade for her display against the 33rd-ranked Garcia.
The steady baseline player was near perfect with her groundstrokes, registering only five unforced errors, as she pressed Garcia into 34 errors and broke the big-serving Frenchwoman six times.
"I think I was playing good tennis from the beginning," she said. "I was very solid from my serves and able to return her huge serves.
"I thought I was really doing a good job from the beginning to the end."
Standing in her way to an elusive berth in the quarters will be either American Varvara Lepchenko or Ana Konjuh of Croatia, both unseeded.
(Editing by Ed Osmond)
