Roberto Martinez hailed his team's battling qualities as they recorded a 3-1 win over Nottingham Forest in the Coca-Cola Championship.
Paul Smith's own-goal gave the Swans the early lead their swift passing game deserved but the visitors equalised against the run of play in the 34th minute through James Perch.
Forest were unlucky to fall behind in the 70th minute when Smith saved Ferrie Bodde's penalty - only for the Dutchman to calmly slot home the rebound.
Swans' substitute Gorka Pintado sealed this clash of the newly promoted teams in the 86th minute, converting a Mark Gower cross.
Martinez said: "We really had to play two games because after a superb first half we went in at 1-1 and then had to do it all again after the break.
"I was very pleased with the performance and although there are areas we must still improve we played some fantastic football today.
"The only disappointment was that we didn't go in at half-time a few goals in front - and that is a lesson we must learn."
There was a huge element of luck with Swansea's opening goal in the seventh minute of this match at the Liberty Stadium.
Jason Scotland slipped a neat pass into Leon Britton, who drilled a shot against the base of the post. The ball rebounded off prone Forest keeper Smith and slowly rolled back over the goal-line.
Swansea were in rampant form but paid the penalty for not increasing their lead when, totally against the run of play, the visitors equalised.
Loan signing Lee Martin swung over a cross from the right, Dorus De Vries in the home goal failed to gather and Perch was left unmarked to slide home.
Honours were even in the second period but the Swans were given a second stroke of luck in the 70th minute when Wes Morgan was adjudged to have fouled Thomas Butler in the area.
With normal penalty taker Scotland off the field Bodde was entrusted with the penalty-kick, which Smith saved - only for Bodde to calmly despatch the rebound.
Substitute Pintado superbly converted Gower's cross to make the game safe for the Swans in the closing minutes.
Martinez added: "We had a little bit of luck with the first two goals but fully deserved our victory.
"We now have competition for places throughout the side and I'm very happy with the strength of the squad."
Forest boss Colin Calderwood conceded that his side were outplayed in the opening period.
"It was an excellent game of football and we played well in the second half, even missing a good chance to take the lead - but it was a poor opening half an hour.
"After drawing level I felt we could go on and win but the penalty knocked us back.
"We will have to improve as we were low-level to begin with and we must bounce back for our next match."