The three points helped Andre Villas-Boas' side open up a seven-point gap between the clubs in the race for Champions League qualification.
Gareth Bale bagged his 10th goal in his last eight games to hand Spurs the lead before Aaron Lennon doubled their lead two minutes later in a crucial spell that proved enough to help them leapfrog Chelsea into third with ten games remaining.
Per Mertesacker's 51st-minute header, which took a huge deflection off Bale, brought the Gunners back into the game but the hosts held on, much to Dawson's delight.
"It's massive to go seven points clear, in a North London derby, to get three points is massive but we have a long way to go, but it is a good day," Dawson said on Sky Sports 1HD.
"We have a great squad and we showed that today.
"It probably wasn't our best performance. We didn't keep the ball like we know we can but showed great determination and we got the three points we deserved.
"We want to be back in the Champions League. I think we showed that in the celebrations after. The fans will go home happy and have the bragging rights at work tomorrow."