Radwanska appeared to be in complete control, dominating the first set. But Torro-Flor rallied, nearly pushing the match into a second set tiebreak.
The Spaniard fought off match point twice, but mistakes would be her undoing. She double-faulted a whopping 10 times, and committed a total of 38 unforced errors to Radwanska's 10.
Radwanska, who has reached the fourth round of the US Open thrice in her career, will face Anastasia Pavlyuchenkova in the third round.