The 31-year-old, who could have left the club during the summer transfer window, netted a superb second-half volley to secure bragging rights for Gunners fans.
Arsenal had taken a first-half lead when Flamini tucked the ball in from close range following a parry by goalkeeper Michel Vorm.
Spurs, though, rallied after the restart and were level on 56 minutes when Callum Chambers deflected a cross from Nacer Chadli past his own goalkeeper David Ospina
However, it was Arsenal - beaten at Chelsea in the Barclays Premier League on Saturday - who finished strongly, with Flamini crashing in a fine 25-yard effort on 78 minutes following a ballooned clearance by Spurs defender Federico Fazio to send the travelling support into raptures.
"You do not expect Mathieu Flamini to score two goals but he was certainly frustrated for a long time and he went for it," said Wenger.
"He has worked very hard recently and I saw in training he was very focused, that he had come back to a good level, also I wanted to strengthen our defensive midfield.
"He is a fighter, Mathieu, and a winner as well.
"I told him at the start of the season it might be difficult for him to be a starter, but he decided to stay and he did fight."
Wenger was pleased with the way his team, which included several changes from the starting XI at Stamford Bridge, secured a hard-earned victory.
"Overall we responded well mentally and physically to the challenge we faced tonight, and it was a convincing performance," the Arsenal manager said.
"We were unlucky with the own goal and after found the resources to score a second goal."
Tottenham manager Mauricio Pochettino felt his side had done enough to get a positive result.
"It was a missed opportunity because we dominated the second half and had the better chances," he said.
"In general the performance was very good and I am happy with the effort from my players, but both goals we conceded were a bit lucky maybe
Also we made some mistakes but this is football."
Pochettino defended his decision to select the likes of both Vorm and Fazio, a player who came close to being sold in the summer.
"It is a competition which is a good opportunity for him (Vorm) and we need to show more respect," the Spurs boss said.
"Look at Arsenal - they played Ospina and is the result is on the other side, then it would be the same question for Wenger.
"He deserves to play."
Pochettino continued: "I don't regret (my selections) - you can make mistakes, remember when (Diego) Maradona missed a penalty? These are big players but this can happen, they are not machines.
"We need to take a lot of positive things
Yes, our supporters and us will feel very bad, when you play against your sporting enemy you want to win more, but this is football
"We need to be happy in the way we played and disappointed with the way we lost the game, but now we need to prepare for the game on Saturday against Manchester City, when we will have one day less to prepare."
Following the final whistle there were some disturbances in the away end, with Arsenal supporters seen pulling down Tottenham signs.
Source : PA