Mauricio Pochettino claimed bragging rights in the final North London derby at the stadium, with goals from Dele Alli and Harry Kane ensuring that Spurs will finish above the Gunners in the table for the first time since 1995.
Tottenham now have only one match left at White Hart Lane before they move to Wembley while their new stadium is being completed, with that coming against Manchester United in a fortnight's time.
"It was a very good game from everyone, from start to finish. It was the perfect day to put on a performance and I'm very proud of it. We knew we had to focus," Vertonghen told reporters.
"It was the last North London derby at the Lane and that's so special for so many people. I know what it means. It was a very big day and we've one more to come. Let's hope we can make that one special too."
Tottenham have now won their last 16 matches in a row at White Hart Lane and are unbeaten at the stadium all season.