Swansea's Gorka Pintado celebrates the opening goal at Histon
Swansea advanced to face holders Portsmouth in the FA Cup fourth round after surviving a late rally at Histon.
Gorka Pintado opened the scoring when the non-leaguers gave him excessive space, the Spaniard having time to turn and tee-up a 25-yard right-foot blast.
Andrea Orlandi tormented debutant Marlon Patterson on the flank, and his cross let Guillem Bauza stroke home.
Pintado missed a late penalty, and soon after Josh Simpson struck to give the Swans a nervous last few minutes.
Mat Mitchell-King directed his header back across goal and Simpson stole a yard in front of his marker inside the six-yard box before smashing the ball past Dorus De Vries.
There were plenty of worried Swansea supporters, their club having gone out to non-league Havant and Waterlooville in last year's third round.
Martinez pleased to overcome Histon
But Roberto Martinez's men held out to extend their unbeaten run to 10 games and to set up a fourth-round trip to Fratton Park.
The build-up to the match at the Glass World Stadium had been controversial as the original date had been postponed due to a frozen pitch.
Blue Square Premier side Histon - in the third round for the first time - accused Swansea of putting pressure on the Football Association to make the decision, although they later apologised.
Histon manager Steve Fallon:
Histon boss rues missed chances
"We had three or four good chances in the first half and might have taken them.
"When they come along in games like these you've got to take them. Swansea had a lot of quality about them, and their finishing was very good.
"But it's a credit to the lads that they are disappointed to have lost to a Championship team.
"Now comes the hard part of picking the players up when all the publicity ends."
Swansea manager Roberto Martinez: "I'm extremely proud, the players had to adapt to the conditions, it takes a lot of character and maturity.
"Andrea Orlandi has had a stop-start season with injuries, it's great to see him out there enjoying himself - he's one of those players who puts a smile on your face.
"I'm looking forward to Portsmouth, more than anything for the fans. We haven't had that glamour for a few seasons.
"It's great to play the cup holders in any competition. It's a great challenge and a glamorous tie to look forward to."
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