The Clarets' contingent of Republic of Ireland internationals will find out next Tuesday who will stand between them and a place in the World Cup finals.
But the joy of the Irish meant disappoinment for Turf Moor team-mate Sam Vokes, whose own hopes of a place at Russia 2018 were dashed in Cardiff.
Ireland's 1-0 win saw them pip Wales to second place in Group D to book a place in the play-offs.
The draw for the two-legged knock-out ties, to be played in November, will take place in Zurich on Tuesday, 17 October.
Clarets' striker Vokes came off the bench to try and rescue Wales' hopes of reaching a first World Cup finals since 1958.
But Chris Coleman's side could not claw back a 57th-minute goal from James McClean, which was set up by Burnley midfielder Jeff Hendrick.
"We knew it would be hard, but when it comes down to one game, the spirit in this group, we can do anything," said Hendrick.
"We always said that once we had one game it’s a do-or-die and when it comes to the big games this group of lads show up.
“I think everybody that plays us knows they are in for a hard game. We might not pass the ball as much as other countries but we’ve got the spirit and it’s great to do it for the fans.
“We’ve got two big games, we’ve just got to keep going and we’ve got to show that spirit again.”
Ireland, with Robbie Brady back from suspension, snuffed out any possible Welsh comeback with Kevin Long coming on in stoppage time to join Stephen Ward and help secure a clean sheet and make it a famous night for the four Clarets.
Sam Vokes was denied a second appearance at a major finals
Burnley team-mate Jon Walters missed out through injury but will now hope to play a part in Ireland's first appearance in the finals since 2002 if Martin O'Neill's side can negotiate the play-offs.
Vokes, meanwhile, hopes to bounce back from the disappointment and go again for the next European Championship qualifying campaign after helping Wales reach the last four at Euro 2016.
The striker, who won his 53rd cap, said: “I thought we had a great campaign and it was all on tonight. So it’s devastating in the dressing room and a tough one to take.
“Ireland made it very hard for us. They got the goal and it was always going to be hard to break them down from that point.
“But we can hold our heads up high and move on.
“The success we had in France makes us want it more so we will be coming back next campaign ready to do it again."
One Burnley player already guaranteed a place in Russia is winger Johann Berg Gudmundsson, whose second goal in two games helped Iceland beat Kosovo 2-0 to top Group I and reach the finals for the first time.
Iceland will become the smallest country to play in the tournament as they look to repeat their heroics from Euro 2016.
"Russia we are coming," Tweeted a delighted Gudmundsson.