The Gunners' first win at White Hart Lane since September 2007 was far from easy and, in fact, they were fortunate to leave victorious.
Tomas Rosicky's thunderbolt after just 72 seconds proved enough in a tense north London derby, which only ended 1-0 thanks to Spurs' wayward finishing and some wonderful defending.
Wenger was proud by the resilience shown by his side in a victory that sees Arsenal move into third in the standings and crucially closes the gap on leaders Chelsea to four points.
"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."
Wenger was quick to highlight the "exceptional" centre-back pairing of Laurent Koscielny and Per Mertesacker for helping Arsenal over the line at White Hart Lane.
The result was the ideal response to the defeat at Stoke in their last Premier League outing and may well prove a catalyst to success in next weekend's trip to leaders Chelsea.
"It gets us a bit closer to Chelsea and makes the game next week even more interesting," Wenger said.
"We are now back to four points behind, we have a game in hand and we've played two away games on the trot now.
"We have five games at home and we will see. It makes, of course, the next game a very big one.
"We needed the three points after a disappointing result at Stoke and I think that was still on our mind.
"Overall, we know to stay in the race it was vital to win and our away fans have been brilliant since the start of the season."
Tottenham head coach Tim Sherwood struggled to contain himself at times at White Hart Lane and at one point threw his gilet at the dugout in anger.
Despite that frustration and the fact Spurs have now lost three in a row, he could have few complaints with his side's effort.
"After going behind to early in the game, you fear the worse but they did me proud today," Sherwood said.
"They stuck together and took the game to Arsenal. We're talking about a team pushing for the title here and we didn't deserve to lose that game. I think we deserved to win it.
"To be honest, I am winner. I want to win and I would rather play bad and win the game.
"Anyone that saw that game today will know we didn't deserve to lose that.
"They had one shot in the second half, when Mertesacker forced Hugo Lloris into a good save.
"They came here to counter-attack and that is a credit to us. They did that pretty well in the first half but the boys stuck to their guns, we showed some quality.
"We should have scored, it's as simple as that. When we score, we go on to win the game because the momentum would have taken us there.
"The crowd were fantastic, stuck with us all the way today and you would expect that when they are seeing the boys give that sort of effort."