In steamy temperatures, the Wimbledon runner-up was too consistent and too battle-hardened for the world number 27 as she won through in one hour, 38 minutes.
Jankovic has slipped down the rankings since she hit world number one in 2008 but at her best, she is a match for Radwanska, as the Pole admitted.
"She's a very consistent player," Radwanska said. "We played against each other a couple of times and they were always long and tough matches. I was prepared for that.
"Especially with the hot conditions, you really have to fight more yourself than against the opponent, because today was really hot."
Radwanska admitted that sometimes it was as if she was playing against a mirror, so alike are their styles.
"We play a little bit similarly," Radwanska said. "That's why I think we always playing long rallies, long games, long points."
Radwanska said she expects to see Jankovic back up nearer the top of the rankings sooner rather than later.
"She was number one and she was in the top four for a long time. In tennis, you can't really play amazing all the time," she said.
"Now she's coming back (to her best). She really was playing good today. If she's going to play like that, she will be back (toward the top) soon."
Radwanska now plays Italy's Roberta Vinci, who upset 13th seed Dominika Cibulkova of Slovakia 6-2 7-5 to reach round four.
"She's another tough opponent, no mistakes at all," she said. "A lot of slices, spin, and then suddenly some strong hits. Against her I just have to do everything (well).
"The last time we played, I think it was Madrid. It was clay, but that clay was faster than the hard courts here."
Serena Williams gained a measure of revenge as well as a place in round four as she beat Ekaterina Makarova of Russia 6-4 6-0 in a tougher encounter than the score suggests.
Makarova beat Williams at the Australian Open in January but the Wimbledon and Olympic champion turned the tables and needed one hour, 21 minutes to advance to the last 16 at Flushing Meadows.
"I felt like I played better today," Williams told the crowd inside Arthur Ashe Stadium.
"I played such a good opponent - she beat me at the Australian Open so I knew going into today I needed to play better and I definitely felt like I played a little better."
In scorching conditions, the left-handed Makarova gave three-time champion Williams plenty of trouble and hung in well in the face of some heavy hitting from the American.
The first four games alone lasted 20 minutes but eventually Makarova buckled under the pressure and Williams gained the crucial break in the 10th game to take the set.
"I was trying to get that break the whole time - but (at the end of the second set) I started playing a little better and a little more consistent," she said.
An early break in the second set broke the resistance of the world number 42 and Williams, who hit eight aces and 31 winners, eased to victory.
The fourth seed now plays Andrea Hlavackova of the Czech Republic.
14th seed Maria Kirilenko bowed out in the last 32 after being surprised 5-7 6-4 6-4 by Hlavackova, who beat her second seeded opponent of the tournament.
Williams turns 31 later in September but said she had no intention of following Andy Roddick and Kim Clijsters into retirement.
"I am nowhere near close to retiring," she said. "Now that Andy and Kim are gone I feel like I have to stay out here. I'm not going anywhere."
Elsewhere in the day's play 6th seed Angelique Kerber wasted little time in beating Olga Kovortsova 6-2 6-1 on Louis Armstrong, while her fourth round opponent Sara Errani also whipped through her match on Court 17 against Olga Puchkova in less than an hour 6-1 6-1, as her Russian adversary rained down unforced errors.
Ana Ivanovic defeated American teenager Sloane Stephens. The former French Open champion was a 6-7 6-4 6-2 winner in two hours and 21 minutes to advance to the round of 16.
Stephens had beaten another former titleholder at Roland Garros, Italian Francesca Schiavone, in the first round at Flushing Meadows but was edged out by Ivanovic in a match punctuated by 11 service breaks.
Ivanovic blasted 37 winners, including 22 off her forehand, to turn the match around after a fast start from the 19-year-old Stephens.
"She's improved so much, she's very dangerous and she's going to be a great player," Ivanovic said.
Serbia's 12th seed will next play the unseeded Tsvetana Pironkova from Bulgaria for a place in the quarter-finals.
Pironkova almost snatched defeat from the jaws of victory, but held on to dump out Silvia Soler-Espinosa 6-1 6-7(3) 6-3. The Bulgarian, a former Wimbledon semi-finalist, had let by a set a two breaks of serve before surrendering her advantage, but recovered in time to win through.
Pironkova awaits the winner of the evening match between Ana Ivanovic and Sloane Stephens.
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