Tomas Rosicky's spectacular early strike was the difference at White Hart Lane, as the Gunners held off a second-half Spurs onslaught to triumph 1-0.
The win was Arsenal's first at the home of their bitter rivals since September 2007 and narrowed the gap on leaders Chelsea to four points.
Wenger leads his men to Stamford Bridge next weekend for a pivotal encounter with renewed confidence brought by victory in the north London derby.
"It is a huge result," the Arsenal boss said. "We were under pressure to win before the game because of course it was a very important game.
"Our early goal maybe influenced too much how we played because we missed a second goal and after that we wanted to protect the lead and sometimes we were under pressure.
"Tottenham played well, we must say. For me, they were absolutely up for it and we needed some special resilience to get away with it.
"As long as we didn't score the second goal, of course it was a very tight game, but in the end, for us, it is three massive points."
The result kept Arsenal's title ambitions alive but effectively ended Spurs' top-four ambitions.
Tim Sherwood, animated on the touchline throughout, conceded the seven-point gap to fourth-placed Manchester City is likely to be too big to breach - something that may well see the head coach lose his job in the summer.
The 3-1 home loss to Benfica in the first leg of their Europa League last-16 tie also means this will likely be another trophyless season for Spurs, but Sherwood vowed to give fans something to smile about before the season's end.
"I think it was difficult anyway," Sherwood said of reaching the top four. "We're just going to try and accumulate as many points as we can.
"Obviously we have a tough game away at Benfica on Thursday and then we play here and we need the same performance against Southampton. If we do, we will win the game.
"We will win probably more than we lose between now and the end of the season.
"This was always going to be a tough period for us but there is no crisis here.
"We lost to Chelsea, who are a lot of people's favourites to win the league, and in the first half of that game I thought we were really, really good.
"The capitulation I spoke about I wasn't happy with and Benfica was obviously going to be a tough game and it went against us.
"Then we were playing Arsenal in a derby and we wanted to win the game and I think we deserved to.
"I have learned more in this last week about being a manager than I learned over the easy period when we were winning games every week."