The Belgian swept Kyle Walker's pass beyond Gerhard Tremmel in the 75th minute to register his first Premier League goal since moving to White Hart Lane from Ajax this summer.
Spurs have lost eight points from winning positions this season but Vertonghen feels his colleagues have finally learned their lesson.
He told Sky Sports 1: "(My goal) came at the perfect time. I think Swansea play good football and were strong at the end.
"We were concentrating until the end because we know what happened in six or seven other games. It's a good win and we're back in the top four now."
Striker Jermain Defoe remains optimistic Spurs can compete for a top-four berth as long as concentration levels remain high.
"It's going to be difficult with the other teams around us because its a strong league," he said.
"But it's important to look at ourselves and just keep winning games, that's all we can do. We'll see what happens.
"It's well known that we've been conceding late goals but it was a fantastic performance from the lads today [Sunday].
"It was difficult to concentrate towards the end they put us under a lot of pressure. It's something we've worked on during the week to be honest.
"Even though we've conceded late goals in the past we were confident of getting three points today [Sunday]."