The world number 10, in her first tournament in five weeks following a foot injury, will now face local favourite Alize Cornet.
The Pole said she had a point to prove at Roland Garros after her 2016 meltdown -- when she squandered a 6-2 3-0 lead in soggy conditions - in a shock fourth defeat against Tsvetana Pironkova.
"Unfinished business, you said it well," Radwanska told reporters when asked about her 2016 exit. "I am hoping the weather stays like that this time. I feel good in this heat."
On Thursday, Radwanska was taken by surprise in the first set on a sun-drenched Court Suzanne Lenglen when the aggressive Belgian, ranked 103 spots below her, went 3-1 up and squandered four break points to go 4-1 up.
Despite fighting back, the Pole could not handle her opponent's big kicking serve and stream of drop shots and Van Uytvanck bagged the tiebreak with a smash.
"She started very well and on clay she can do a lot of things," Radwanska said. "She was mixing up a lot of shots. She can hit the ball really well.
"In the second set I had to play my game and not wait for her mistakes."
Radwanska, whose best grand slam performance was reaching the 2012 Wimbledon final, decided to change tactics and mixed it up as well, rushing to the net more often and attacking the Belgian's high-bouncing serve early to race through the second set 6-2.
The 23-year-old Van Uytvanck, who underwent wrist surgery in December and has made only one WTA main draw appearance this year prior to Roland Garros, was broken in the third game and the Pole never looked back.
Radwanska won her match when her opponent dumped a backhand into the net after two hours and 23 minutes.
"Clay is not my favourite surface. I am not expecting miracles here but I will try my best," she said.
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
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