Spurs needed to beat their fierce local rivals to keep the gap at four points following leaders Chelsea's win earlier in the day - and they did just that as the Gunners slipped to a ninth defeat of the season.
After a goalless first half in which Dele Alli and Christian Eriksen missed good chances for the hosts, the former opened the scoring on 55 minutes before Harry Kane converted a penalty just 146 seconds later.
The win means Tottenham will finish ahead of Arsenal for the first time since 1995.
With Tottenham's new stadium being built around their current home, this marked the last time Arsenal would make the short trip to White Hart Lane - but it was only a day to savour for their hosts.
Arsenal had seen both Manchester United and Manchester City drop points in the race for the top four - but Arsene Wenger's men could not capitalise.
Although Pochettino has become the first Spurs manager since Gerry Francis to guide his side to finish above Arsenal, the Argentinian was more concerned with the attempt to reel in Chelsea.
"I feel very proud, first of all because the players played their best and they were fantastic," he said.
"And for our fans, I feel very happy for them. It was a fantastic game and yes, we are in the race for the title. We reduce again the gap to Chelsea.
"Now we have to be focused because we have again on Friday a very important game against West Ham and now it's important to be focused on that game.
"I am happy as, when you play a derby like Tottenham versus Arsenal, always it is important to win.
"But I have massive respect for [Arsene Wenger]. I admire him for what he is doing at a club like Arsenal and it is a fantastic job.
"I am so happy but our challenge is and our aim is not only to beat Arsenal but also the 19 teams in the Premier League.
"Of course I am very happy but I am so calm as we have four games to play and now is important to be focused and to try to reduce the gap to Chelsea."