The Pole got out of the blocks superbly and went a set up in just 21 minutes, taking it 6-0.
However, in the second set the Spaniard's power started to have a say, but Radwanska had enough in her to take it 7-5.
Read how the action unfolded below.
4.03pmGood afternoon tennis fans. The US Open continues today and first up on Louis Armstrong Stadium is Polish fourth seed Agnieszka Radwanska against Spaniard Maria-Teresa Torro-Flor.
4.05pmRadwanska's opponent is the unknown Torro-Flor, who got past a very tricky encounter against Marina Erakovic, which will have made the Pole sit up and take notice.
4.06pmThe warm-ups are just about finished and we're nearly ready to start. It's all prompt here at Flushing Meadows. The favourite will serve first.
4.06pmSolid start for Aggie, who moves 30-0 up with some accurate early serving.
Radwanska 1-0* Torro-FlorAccuracy is always the name of Radwanska's game and she proves that early on here, patiently waiting for errors until the Spaniard goes long to hand her a hold to love first up. The perfect start.
4.09pmNow she gets into her opponent's serve as well, and is 0-30 to the good. No points dropped thus far...
Radwanska *2-0 Torro-FlorBREAK! This is so easy at the moment for the Pole. She has won eight of nine points so far, with Torro-Flor netting tamely to give up the break.
4.12pmThat's better from the Spaniard, who swipes a forehand winner down the line to edge ahead in the game.
Radwanska 3-0* Torro-FlorBut Radwanska is too strong. She's really finding the corners on both sides and despite being behind in the game she takes it 40-30. It's quickly getting away from the Spaniard.
Radwanska *4-0 Torro-FlorDOUBLE BREAK: This is in danger of being one of the shortest matches of the tournament this year. She has too much in every department at the moment, Radwanska.
4.20pmFine net play from the Pole now, who even manages to run Torro-Flor ragged from the middle of the court.
4.21pmWhat can the Spaniard do? This time Radwanska defends before hitting a passing winner following a smash - just superb.
Radwanska 5-0* Torro-FlorFifteen minutes. That's how long we've been playing. Four points. That's how many the Spaniard has one. This is as one-sided as they come. At this rate a double bagel will be achieved with ease.
4.26pmThe Spaniard is 40-30 up here... A chance for a game perhaps.
Radwanska 6-0 *0-0 Torro-FlorSET! But no. A double fault leads to an advantage, which Radwanksa makes no mistake with a superb return. Just 21 minutes that took and the Pole is half way there.
4.32pmBetter start to the set from the Spaniard, who moves 0-30 up but then wastes a glorious chance of a forehand.
Radwanska 6-0 0-1* Torro-FlorBREAK! She's done it! Not only has she won a game, but she has a break to put her ahead in the set. Brilliant response.
4.37pmJust as the Spaniard is cruising at 40-0, she hits a double fault and two unforced errors to let her opponent right back in at deuce. That's poor.
Radwanska 6-0 *1-1 Torro-FlorBREAK! And if you do that against the top players? They will punish you. Radwanska hangs in again at advantage down, but is too good when she edges in front to level the set.
Radwanska 6-0 2-1* Torro-FlorWhat a brilliant point Radwanska! It's deuce again but she plays every shot under the sun - a drop shot from the squat position followed up with a running winner at the net. Brilliant.
4.48pmTorro-Flor is serving much better here, which is putting her opponent under a lot of pressure. It is the weakness to Radwanska's game playing against the big serve and that's the area the Spaniard needs to keep targeting. She's 30-15 up here.
Radwanska 6-0 *2-2 Torro-FlorIt's Torro-Flor's first hold and she did it in style as well. Much better from the Spaniard, but there is a long, long way back from this point.
4.51pmRadwanska's server, however, has gone off the boil. A couple of unusual errors takes the game to 0-30.
4.54pmHowever the Pole has brought us back to deuce with more accurate hitting. If in doubt, just be patient.
Radwanska 6-0 2-3* Torro-FlorBREAK! Frustration for Radwanska, but professionalism from Torro-Flor. The Spaniard does not let that early setback in the game put her off and she finds a second wind to break again in the set. Can she hold this one?
5pmThere have been a couple of warnings from the umpire for the crowd to hurry up getting to their seats. There's basically no-one here, which is a poor showing for a match involving a world number four. On the court, Radwanska moves 15-30 ahead.
5.01pmNow it's 15-40 as Radwanska again looks to break right back...
5.01pmReally good from Torro-Flor to hit a drive volley overhead for the winner to save the first.
5.02pmDefensive from Radwanska, but it's not enough. In the end Torro-Flor goes for the big forehand and catches the line, taking us to deuce on review. But no, the point is not give because Raswanska stopped - no, she didn't.
Radwanska 6-0 *3-3 Torro-FlorBREAK BACK! That's a lovely cross-court drop from Radwanska, who deceives her opponent to once again break straight back.
5.05pmAgain Radwanska defends accurately with the Spaniard going long with one of her attempted baseline shots.
Radwanska 6-0 4-3* Torro-FlorThe pressure is right on Torro-Flor now as Radwanska wraps up a love service game with the first ace of the match. Suddenly the Spaniard is serving again and really needs to hold.
5.10pmThat's excellent from the underdog. From 0-30 she moves to game point, the final one she set up really well sending her opponent across court for a winner coming into the net.
Radwanska 6-0 *5-3 Torro-FlorBREAK! I said she needed to hold, but she has been unable to. Radwanska remained calm when it mattered to force the vital error and will now serve for the match.
5.13pmShe races 30-0 ahead, and the Spaniard is looking defeated..
5.16pmAt match point down Torro-Flor plays a magnificent, aggressive point and even the rapid Radwanska runs out of juice.
Radwanska 6-0 5-4* Torro-FlorBREAK BACK! Well, I thought she was beaten and I was wrong. She played her best tennis of the match at match point down there and is rewarded with her third break.
Radwanska 6-0 *5-5 Torro-FlorThe unforced error count is 31-9, but the Spaniard here is playing some great stuff. Radwanska has absolutely no answer to her power at the moment and once more we're level in the second.
Radwanska 6-0 6-5* Torro-FlorJust as quickly as they disappeared, the errors have come back. Radwanska wraps up a service game with ease to alleviate a load of the pressure on here. She's at least in the tie-break, but could still take the win with a break.
5.28pmWhen she gets here first serve in, she quite often wins the point, but her second is not good enough. A double fault brings Radwanska into the game at 15-15.
5.30pmMatch point Radwanska here as a review from the Spaniard is incorrect. She went long and has a big serve now...
5.32pmShe's battled back now though and has advantage. But that quickly disappears and we are back to deuce. The quality has really been lacking in the latter part of this set.
Radwanska 6-0 7-5 Torro-FlorGAME, SET & MATCH RADWANSKA!
5.34pmIn the end that took longer that it looked like it would, but the win is what matters. The power of the Spaniard shows where Radwanska is weak, but she can take a lot from that first set.
5.36pmThat's all from us for this one, but please do stick around for all the latest sporting action. Goodbye from me.