Swansea manager Francesco Guidolin at Turf Moor
Francesco Guidolin gave a Premier League debut to new signing Fernando Llorente who helped bring about the goal that broke the deadlock.
Burnley goalkeeper Tom Heaton could only parry the Spanish striker's header into the path of Leroy Fer who poked the ball home with 82 minutes gone. The goal was Fer's first in Swansea colours.
Manager Guidolin was pleased with his team's performance. He said to BBC Sport: "It's a good start against a good team at a difficult ground but we are happy, because this was an important victory and we're more confident for the future."
Swansea City's Leroy Fer celebrates
The Swans were good value for their victory, as they just shaved the possession stats with 53%, whilst with 9 shots on target they can count themselves unlucky that they only managed the one goal.
Swansea supporters will have been encouraged by what they saw only days after inspirational captain Ashley Williams signed for Everton.
They took to Twitter to show their delight at the opening-day win, and to congratulate Fer on breaking his goalscoring duck at the Liberty.
Great 3 points on the road with a clean sheet thrown in for the @SwansOfficial, hope the Jacks traveling army have a safe trip home— Mark Fisher (@mfish_9) August 13, 2016
The Swans host Hull City at the Liberty Stadium next Saturday and will be hopeful of securing a second win against a newly-promoted side in as many weeks against a Hull side who put aside their club's disarray to defeat Leicester City this weekend.