"We are building a reputation at the Lane and it feels good to beat the big teams. It's a good sign we are progressing well," Vertonghen said.
"Maybe everyone thought at the start of the season it would be close with the other teams but you see a proper top six now.
"It means you have to win against your rivals, especially at home, and we've done that twice now, beating City as well here.
"It's a good feeling and we're getting stronger and stronger."
Chelsea had looked virtually unbeatable during their 13-game winning streak but Tottenham were faster, stronger and more aggressive than their London rivals.
"It sends a message, in a good way, we played very well, didn't give chances away," Vertonghen added.
"We sent a message last year as well when we were challenging for the title and hopefully we can do it again now.
"They look at us in a different way in the last two years. I think we are stronger than last year.
"You see who came in, what they are doing for us, how strong our squad is, how strong our bench is. It's unbelievable. Everyone is happy to play for Tottenham."