The 30th seed came through a tight first set 7-5 before breezing through the second 6-0 to book her place in round two.
Read how it all unfolded in our game-by-game updates below.
4.02pmAfternoon all! The final Grand Slam of the year is here and to begin our coverage on SM we have two Brits in action.
4.05pmHere we will be covering Robson's match against Dominguez Lino and if you want to follow Dan Evans's tough opener against 11th seed Kei Nishikori join Darren Plant here.
4.08pmHopefully 19-year-old Robson won't be too affected by her wrist injury. We're nearly ready to go out on Court 17.
4.11pmRobson wins the first couple of points as Lino dumps a pair of groundstrokes into the net.
Robson 1-0* Dominguez LinoA perfect start for Robson as she holds to love, wrapping the game up with her first ACE down the middle.
Robson *2-0 Dominguez LinoBREAK! Brilliant stuff from Robson as she peppers the Spaniard's backhand with her powerful forehand to break serve at 30-40.
Robson 2-1* Dominguez LinoBREAK BACK! Not so good from Robson as she loses her serve to love, slicing a backhand tamely into the net to gift Lino the break back.
4.22pmAlthough she packs a punch, Robson does like a bit of a wobble and that was evident in the last game. She has just hit long with a chance to regain the break.
Robson *2-2 Dominguez LinoLino holds thanks to a fortunate net cord at deuce before her serve down-the-T is returned long by Robson.
4.25pmUPDATE: Over on Court 13, Evans has gone down an early break against Nishikori. Follow Darren's updates here.
Robson 2-3* Dominguez LinoBREAK! Dear oh dear. Robson has lost three games in a row and it's all her fault as she double faults on game point before shooting long with an easy forehand and then double faulting again to gift Lino the advantage.
Robson *3-3 Dominguez LinoBREAK BACK! This isn't the greatest quality! Lino matches Robson in double faulting at break point to allow the 30th seed to level the set. It's a little windy on Court 17 and it seems to be causing havoc with the ball tosses. Double fault count: Robson 3-4 Lino.
4.33pmRobson is looking good at 30-0 but then moves to four doubles as well with a long second serve. It's now 30-30 as the Brit fails to get Lino's drop shot back over.
Robson 4-3* Dominguez LinoRobson holds for the first time since the opening game thanks to her fourth ACE.
4.36pmRobson is the one who is going for her shots and her big-hitting certainly has the crowd on her side. Lino's loopy forehands and low slices are forcing Robson to make all of the running and if she can limit the unforced errors then she should come through this just fine.
4.38pmGreat rally! Robson is all over Lino but the Spaniard stays in the point before grabbing the initiative with a drop shot that the Aussie-born Brit can't get over.
Robson *4-4 Dominguez LinoRobson looks menacing at 15-30 but loses three on the trot as Lino holds serve. On the last two points Robson failed to return the Spaniard's average serve. She can't be doing that.
Robson 4-5* Dominguez LinoBREAK! Not good from Robson. She seems fine at 40-15 but then crumbles on the next four points, gifting the Spaniard the chance to serve out the set with a loose forehand.
4.49pmUPDATE: Over on 13 Evans has broken back against Nishikori. Great stuff from the British number three.
Robson *5-5 Dominguez LinoBREAK BACK! The topsy-turvy nature continues as Robson breaks straight back thanks to a high backhand that diminutive Lino can loop back over the net.
4.54pmBig cheer goes up as Robson saves two break points to bring it back to deuce. Over on 13 Evans has grabbed the set 6-4 against Nishikori. Brilliant!
4.55pm"Come on!" Robson says to herself as she saves another break point after her seventh double fault at deuce.
Robson 6-5* Dominguez LinoThe 19-year-old comes through and will now be hoping to break Lino again to ensure that the opener doesn't go into a tie-break.
5pmRobson's cross-court forehand drops onto the back of the line and she's two points away at 30-30.
5.01pmLino's drop shot arcs out and Robson has SET POINT...
5.02pmShe can't take it after a mammoth rally where both women did all they could to stay in the point.
5.03pmSET POINT number two...
5.03pmSaved again by Lino as she goes into the corner with a forehand before confidently putting away the smash.
5.04pmSET POINT number three...
Robson 7-5 *0-0 Dominguez LinoSET! This time she takes it by targeting the Lino backhand, which eventually slices long. 53 minutes that took.
Robson 7-5 1-0* Dominguez LinoAn assuring start to the second from Robson as she holds to 30.
Robson 7-5 2-0* Dominguez LinoBREAK! Corrrr, what a way to break! Robson steps into a forehand return and rifles it up the line.
5.16pmRobson was up 2-0 in the first set and hardly raced away with it and it doesn't look like she's going to do so in the second at 15-40. Two break-back points for Lino...
5.17pmShe saves the first with a classy one-two, serve-forehand punch.
5.18pmAnd the second! It's a lengthy rally and you might expect Lino to wear Robson down but it's the Spaniard who makes the mistake by slicing long.
Robson 7-5 3-0* Dominguez LinoGood stuff from Robson as she stays calm with her smash after a perfect defensive lob from Lino lands on the baseline. Two strokes later and she comes through a tough game to open up clear daylight in the second set.
5.22pmBy the way, if Robson does come through this then she'll face either Caroline Garcia of France or America's Shelby Rogers.
Robson 7-5 *4-0 Dominguez LinoDOUBLE BREAK! It looks as if it will be a place in round two for Robson as she goes further ahead thanks to Lino's overhit forehand.
Robson 7-5 5-0* Dominguez LinoPhenomenal hitting from Robson as she breezes through that one to love, moving within one game of the match.
5.32pmUPDATE: Blimey oh riley! Evans has just broken in the 10th game, just like he did in the first, to snatch the second 6-4 against 11th seed Nishikori.
Robson 7-5 6-0 Dominguez LinoGAME, SET AND MATCH ROBSON!
5.34pmYet another break and that's Robson through to the second round at Flushing Meadows.
5.37pmIn his match summary, our very own Jack Prescott described the first set as "scrappy", couldn't think of a better word. It was an unconvincing start to her Flushing Meadows campaign but Robson really came into her own in the second and looked much, much better. You can see why Lino's timid style of play has never earned her a victory over a player in the top 35.
5.40pmNext up for Robson will be either France's Caroline Garcia or Shelby Rogers from the US.
5.41pmThanks for joining SM for coverage of this one. Make sure you now head over and join Darren to find out if Evans can complete a memorable victory over Nishikori.