Spurs went into the game knowing that victory would be enough to secure a higher Premier League finish than their rivals for the first time since 1995.
Mauricio Pochettino's side dominated for long periods and made the breakthrough when Dele Alli bundled home after Petr Cech could only parry Christian Eriksen's strike.
Harry Kane doubled the advantage three minutes later and Spurs cruised to a comfortable 2-0 win over the Gunners to keep their hopes of winning the title alive.
Vertonghen was named Man of the Match for his imperious defensive display and the 30-year-old is adamant Spurs' superior desire contributed to their victory.
"It was a massive game in so many different ways," he told Sky Sports News.
"We showed from the start we wanted to win more than them, and that we want to stay in the title race.
"It was a great performance throughout the team, from Hugo (Lloris) to Harry."
Spurs are now just four points adrift of pacesetters Chelsea, who beat Everton earlier on Sunday afternoon.
But Pochettino's side could cut the Blues' advantage to one point if they beat West Ham next Friday and Vertonghen is determined to keep asking questions of Antonio Conte's men.
"We can't do anything else other than keep on winning games and putting pressure on them.
"If we win our game on Friday it'll be down to one point and then let's see what they do," the Belgian insisted.