But Bale pulled a goal back and Cesc Fabregas handled Rafael van der Vaart's free-kick to allow the Dutchman to level from the penalty spot before Younes Kaboul headed home a dramatic winner five minutes from time.
"For the fans and everybody it's the one game everyone looks out for and to get the victory, especially at the Emirates, is something special," Bale told Sky Sports 2.
"The gaffer said before the game we have got a great squad and a great team and we can match anybody. We didn't have the greatest of first halves but showed what we can do in the second half.
"We put JD (Jermain Defoe) up front in the second half, sort of went for it a bit, worked for each other and it paid off."
Bale's team-mate Van der Vaart said on Sky Sports 2: "It was difficult, they put a lot of pressure on us and we didn't play our game. We had some problems, but we were really happy with the second half, it was much better.
"It was my first time here so it wasn't bad, I knew about our away record against Arsenal.
"It's a great day for the club."