A last minute winner from Chris Reed saw Swansea overcome Bristol.
The second half display in particular pleased captain Joe Howarth.
He said: “We played alright in the first half but they put a lot of pressure on us and played a very high line.
“The second half was much better and we were starting to put into place what we’ve been working on in training.”
Despite starting the day in fifth, Howarth maintains that Swansea can mount a promotion push this season.
He said: “We’ve definitely got the quality to gain promotion so we need to make sure we take advantage of our home form.”
In the first minute Bristol came close to scoring when Ben Walters’ powerful low shot just drifted wide of the post.
Swansea responded, a short corner was put narrowly wide and Andrew Willemite’s winding run was halted just in time by the Bristol defence.
Chris Metcalfe went close for Swansea not long after but he failed to fully test the keeper.
The game’s opening goal went to Swansea, as Rory Thorburn raced onto a long pass to slide the ball into the net.
The lead was short-lived however as Adil Dostmohamed tapped in from close range.
The second half proved to be a livelier affair as both teams pushed for the win.
Johnny Cardy went close twice for Swansea before Bristol scored against the run of play. A short corner was smashed towards goal and Cottam tucked in the rebound to make it 2-1.
Swansea could have equalised five minutes later, but Chris Reed could only strike the post after getting onto a defence splitting pass from Thorburn.
Reed was impressive throughout and showed some great skills with the stick getting behind the Bristol backline.
Eventually Swansea did equalise when Thorburn grabbed his second of the game, prodding the ball home.
With the game’s coming to a close, Swansea persevered and Cardy’s pull back was met by a sliding Reed to ensure the win for the South Wales side.