The visitors took a 56th-minute lead against the run of play at the Emirates Stadium on Saturday, as Nacer Chadli netted his fourth Premier League goal of the season.
But with 14 minutes left, Oxlade-Chamberlain - preferred to Alexis Sanchez in the starting XI by manager Arsene Wenger - was in the right place at the right time to slam home from inside a crowded penalty area.
"1-0 down in the Spurs derby is always a bit nerve-wracking because you never want to lose the game," the England international told Sky Sports.
"I thought we did well to come back, but when we made it 1-1 I really did think we could we push on and get the winner.
"We knew, first and foremost, we had to compete with them because that's what derbies can be like.
"Sometimes it's not about the best football; it's about who wants to win it more. We came out in the second half, nerves were settled down a bit and we started to pass the ball better and get into the game more."
The result means Arsenal are unbeaten in six Premier League outings this term, but four of those matches have ended in draws.
"We would have liked to have played some better football but it is important that we are not losing games," Oxlade-Chamberlain added. "First and foremost, we have to defend and then the more fluid side of our game will come."
Despite his considerable attacking talents, the goal was Oxlade-Chamberlain's first since Arsenal's 2-1 FA Cup victory over Liverpool in February and the 21-year-old revealed that he had bemoaned his luck in front of goal before the match when talking to his father and former England player Mark Chamberlain.
He added: "I said to my dad before the game, 'The law of averages says I've missed enough chances. Now, surely it's time I scored'.
"I'll be working on scoring more as I have the potential to do that, but I also have my role to do defensively."
