Forward Hal Robson-Kanu said Wales' victory over Belgium was the culmination of months of hard work and boss Chris Coleman's tactical nous.
Friday's 1-0 Euro 2016 qualifying win gave Wales a three-point lead over their opponents at the top of Group B.
With four games remaining, Wales are on course to reach their first major finals since 1958.
"The manager has been absolutely incredible, I absolutely love playing under him," said Robson-Kanu.
"He knows what the boys need, what the team needs, he gets the tactics right and he motivates the boys for every game."
Four years ago Wales were 116th in the Fifa rankings, and they were among the bottom seeds in the last World Cup qualifying campaign, alongside countries such as San Marino, Andorra and Luxembourg.
But Coleman's side will now enter the top 10 for the first time and will be among the top seeds when the 2018 World Cup qualifying draw is made in July.
Coleman became Wales manager in January 2012 and lost his first four matches in charge.
The former Fulham and Coventry boss was the subject of sharp criticism, with his position being questioned.
But steady progress was made from that point and Wales are unbeaten in six matches in the current campaign.
"Obviously at the start it was tough, we had to get some momentum going," Robson-Kanu told BBC Radio Wales Sport.
"But we did that and you have to give credit to the manager and the staff for what they've done."
Robson-Kanu said Coleman and his staff have turned the "whole vibe of the place into a positive one".
He added: "We're showing we can consistently produce performances, which is what's required, and we're looking forward to the future."
Wales' rise culminated in their victory over Belgium, who were ranked second in the world before the match in Cardiff.
The Red Devils prepared for the game by beating France in a friendly, while Wales had a prolonged training camp.
Robson-Kanu, usually a winger for Reading, was deployed as a lone centre-forward against Belgium - his hard-working, physical presence providing the foil for the talents of Real Madrid's Gareth Bale and Arsenal's Aaron Ramsey.
"The manager and the staff got us in early - two weeks before the game. It's not really common to do that, but they thought that preparation was required and they were spot-on again," added the 26-year-old.
"The build-up was intense - we had to put in the work, but when you have nights like that you're happy to put in any amount of work.
"We'd been working on the way we needed to play; the manager wanted me to stretch the pitch, cause the centre-halves a lot of trouble and I did that.
"That allowed Bale and Ramsey to receive the ball in some space.
"Going into the second half, the last 10 minutes of the game the boys were putting their lives on the line for the win and it showed.
"The crowd, the atmosphere, that was something I've never experienced before and they really got us over the line.
"It was a fantastic night but hopefully one of many more to come."