The scoreline flattered Nottingham Forest who were thoroughly beaten by a well-organised, confident Swansea side.
Swansea dominated much of the first half and looked comfortable with a two-goal lead. But Forest fought back towards the end of the half, getting a late goal back and coming close to a second.
Swansea increased their lead in the second half and could have scored more while Forest struggled to find any shape to their side and threatened only occasionally and a stoppage time goal was too little too late.
A good break by Stephen Dobbie gave Swansea the fist real chance of the game and Wes Morgan did well to block his effort.
A foul on Radi Majewski gave Forest a free kick a long way out and as Chris Cohen's ball came into the penalty area Tyson tried a diving header but couldn't make contact with the ball.
Swansea were dangerous on the attack with a good through ball by Dobbie to Scott Sinclair whose shot from just inside the box sent Lee Camp diving low to his right to make the save.
Forest's first chance came when Wes Morgan set up Kris Boyd whose shot from just outside the D forced a save from Dorus De Vries.
A superb goal by Sinclair gave Swansea the lead when the ball landed for him in midfield. He made a run down the left and into the D, working his way right across the box to get past the Forest defenders before turning and putting the ball into the net.
And they doubled their lead five minutes later after good run down the right by Angel Rangel who beat Nathan Tyson to get the ball into the penalty area. Morgan blocked the first effort but it fell for new loan signing Fabio Borini and in spite of four Forest players blocking his path he fired the ball diagonally across the goal and into the far side of the net.
A great break from Swansea carved Forest open and when the ball was crossed out to the right of the box for Borini his effort crashed off the post.
Forest had a chance late in the half from Tyson's cross to Boyd whose effort was only just wide.
And Boyd came close with another effort from 18 yards but that was put out for a corner.
And Boyd finally got the ball in the back of the net a minute before half time after some patient build-up play. Tyson got the cross in from the by-line and Boyd turned inside the 6-yard box to slot the ball past De Vries.
And they came close to a stoppage time equalizer from a free kick. Majewski's shot came in well and Luke Chambers looked like he was going to head the ball in but it was put out for a corner.
Garath McCleary came out for the start of the second half in place of Majewski.
It was a good attacking start by Swansea with Dyer making a great run down the right and into the box where he went down without a touch from a Forest player.
And they forced a good save from Camp who could only tip the ball over for a corner from Dobbie's shot from the edge of the penalty area.
Swansea went three up 13 minutes into the half when Dobbie made the run down the left and worked his way through two Forest players before getting his shot in. Camp was able to block his effort but it came back out to Borini who side-footed the ball into the net.
Dyer came close to getting their fourth when he was allowed too much space to shoot from the edge of the D. The ball was headed for the top of the net but Camp reached high to tip it over.
Forest's second substitution saw David McGoldrick come on for goalscorer Boyd.
Swansea continued to threaten and missed a great chance for a fourth goal when Sinclair got past Anderson but then shot high and wide from ten yards out.
A good through ball by McGoldrick created a rare chance for forest and Cohen's shot, as he broke into the box, forced a good save from De Vries.
A surprising third substitution for Forest saw Julian Bennett make his long-awaited return, taking the place of Konchesky who headed straight down the tunnel.
Swansea missed another chance when they were gifted the ball on the right and the ball fell for Borini who had Camp beaten but shot into the side netting.
Forest had a late chance from a free kick when the ball was floated in to McGoldrick who stabbed it towards goal and claimed that De Vries had carried the ball over the line, but the referee was not convinced.
Forest got one back in stoppage time when McCleary beat his man on the left and crossed to Paul Anderson who side-footed the ball past De Vries and into the far corner.
And a diving header from Anderson almost gave them a late equalizer but, with the keeper beaten, his effort hit the post.
Nottingham Forest: Camp, Gunter, Morgan, Chambers, Konchesky(Bennett 77min), Cohen, McKenna(C), Majewski,(McCleary 45minHT) Anderson, Tyson, Boyd(McGoldrick 63min)
Subs not used : Darlow(GK), Moloney, McGugan, Adebola
Bookings: Anderson 34min, Konchesky 48min, Cohen 53min
Scorer: Boyd 44min, Anderson 90+3min
Swansea City: de Vries, Rangel(Monk, 78min), Taylor, Tat (C), Williams, Allen, Gower, Dobbie(Britton 69min), Sinclair, Borini, Dyer(van der Gun 88min)
Subs not used: Ma-Kalambay, Pratley, Orlandi, Moore
Scorer: Sinclair 21min, Borini 26min, 56min