The Swans pretty much finished the tie off in the first half with goals from Gorka Pintado and Guillem Bauza and could even afford the ‘luxury’ of a missed penalty before Histon pulled one back before time.
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. (continues below)
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.
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.