Goals from Jan Vertonghen and Gareth Bale put us in the driving seat in the first half at the Liberty Stadium.
Swansea hit back through Michu with 20 minutes remaining and stepped up a gear in search of an equaliser but we held firm.
Indeed, the home team only really created one more chance of note in the final minute when Nathan Dyer met Wayne Routledge’s cross only for Gareth to slide in and block.
If anything, we looked more likely to score on the break as Michel Vorm denied Gareth and Jermain Defoe and Gareth struck the post.
“Swansea put us under pressure the longer the game went on,” said Scott. “They are a very good team and we had to show a different side to our character at the end.
"We did that to grind out the result.”
It was a key win – our ninth on the road in the Premier League this season – and Scott insisted the result was all that really mattered after a run of 12 matches unbeaten was halted by successive defeats.
“It’s massive result for us,” added the midfielder. “Before the game started, winning was always going to be the most important thing and we managed to come away with the three points.
“That was crucial after a couple of defeats in the league, we’ve stopped the rot, picked up a big win and now we move on again.”