First-half goals from Gareth Bale and Aaron Lennon were enough to secure the win as Spurs leapfrogged Chelsea back into third place in the Premier League table.
Dawson, who was imperious alongside centre-back partner Jan Vertonghen, believes the result is huge for the club and has boosted their chances of qualifying for the Champions League.
“It’s massive,” the 29-year-old told Sky Sports after the match. “Seven points clear, north London derby, to get three points is massive. Still a long way to go, but it’s a good day.
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“To be a north London derby, the fans will go home happy, they’ll have the bragging rights at work tomorrow, and everyone goes home happy.”
Tottenham held a similar advantage over their north London rivals last season, but forfeited third place to the Gunners, but Dawson believes Spurs are stronger this year.
“We’ve got a great squad, a great team, we showed that today,” the defender continued.
“It probably wasn’t our best performance, we didn’t keep the ball like we normally can, but we showed some determination and got three points which we deserved.”
Vertonghen, who excelled against Arsenal, was delighted to win his first north London derby at White Hart Lane, and agreed with his captain that Spurs are a different proposition this year.
“I just arrived here six months but you can feel this is one of the most important games of the season,” said the Belgian after the match. “It’s a north London derby and my first win, so I’m very happy.
“We know we can defend, we are a very strong team, we can play compact and we showed it again.”