The full-back joined the League One side on loan until January on Monday.
He was thrown straight in at the deep end for the visit of the Premier League team in the third round encounter at Broadfield Stadium.
Nathan played the full 90 minutes as Crawley came from 1-0 down to lead 2-1, only for Swansea to to hit back with an equaliser on 74 minutes before grabbing the winner in injury time.
Danny Rose put in another full shift for Sunderland as the Black Cats negotiated a tricky third round tie at League One side MK Dons. They recovered from losing Lee Cattermole to a red card in the first half to win 2-0 at stadium:mk.
Meanwhile, John Bostock was an unused substitute as League One Swindon produced another upset in the competition, beating Championship side Burnley 3-1 at the County Ground.
Simon Dawkins scored a cracking goal as San Jose Earthquakes moved closer to clinching the Supporters' Shield in the MLS.
The attacking midfielder - playing on the left for Earthquakes - smashed home a 25-yarder inside two minutes of Sunday's 2-1 win at Seattle Sounders.
The victory sees our partner club top of the Western Division by 11 points and leading the race for the Supporters Shield by five points from Kansas City.
The Supporters Shield is awarded to the team with the best regular-season record in the MLS.
The top five teams from the Western and Eastern Division qualify for the play-offs.
Back in the UK, Danny Rose played the full 90 minutes as Sunderland conceded a late goal in a 1-1 draw at West Ham in the Premier League. Harry Kane didn't feature in Norwich's 1-0 loss at Newcastle.
Massimo Luongo played a full shift as Ipswich suffered a 2-1 home loss to Charlton in the Championship - he's in action against Charlton's Salim Kerkar below.
In League One, Ryan Fredericks made quite an impact in a 20-minute substitute appearance in Brentford's 1-0 win against Oldham, forcing a save from Dean Bouzanis and then setting up a chance for Farid El Alagui that was cleared off the line. John Bostock didn't feature in Swindon's 4-0 win against Bournemouth.
In Greece, Bongani Khumalo played 90 minutes as PAOK made it three wins in four to move second in the Super League, this time a 3-0 victory at Xanthi.
David Bentley also played 90 minutes as FC Rostov lost 3-1 at Spartak Moscow in the Russian Premier-Liga.