LEE TRUNDLE'S 15th goal of the season secured Swansea's progression with a narrow win over Stevenage.
Kevin Nugent gave the home side a 23rd-minute lead, but the Conference side hit back shortly after half-time through Anthony Elding, only for Trundle to immediately regain the lead
Stevenage manager Graham Westley though, was proud of his side, despite their narrow defeat.
"My players put in a good 90 minutes and I thought we were unlucky not to have at least forced a replay," he said.
"Now we can concentrate on continuing our improvement and moving up the Conference table into the promotion race."
The Swans were hoping to build on indifferent league form that has seen them slip from the Third Division automatic promotion places.
And it was the Vetch Field outfit that made a perfect start.
Nugent was the first to react after Andy Robinson's shot was parried, and the veteran striker hammered home from six yards to score his sixth of the season and give Swansea the lead.
The home side had already had chances to put themselves in front. Highly-rated young defender Richard Duffy broke forward to have a shot saved by Lionel Perez, and later fired wide of the post.
Westley's men had also gone close early on - Steve Watson and Dino Maamria each hitting shots that missed Roger Freestone's goal. …