McLaren's Button lost track position to the Force India of Perez at the pit stops, prompting the Briton to attack in the closing stages of the Grand Prix.
"I had an amazing battle with Checo [Perez] - we took the first Lesmo side by side, which doesn't happen very often,” enthused Button, who eventually came home half a second behind the Mexican.
"It's a pity I couldn't get past him - I tried so many times, but he was so strong under braking that to match him into the turns I was locking up the fronts and the rears, which left me struggling for position on the exits. I was really on the limit.
"It was superb wheel-to-wheel action - I hope it was great entertainment for the spectators and fantastic TV for the fans at home.”
Perez meanwhile said his trust in Button's ability and the Briton's fairness behind the wheel had contributed to the pair's fight.
"The race was a lot of fun - we were always fighting somebody and always pushing hard,” Perez said.
"It was great racing and it's good to score important points for the championship. The most important part of the race was the fight I had with Jenson, which was really nice and reminded me of the old days.
"I know he is a driver that you can fight really hard and it's always clean.
"At the end of the race with Kevin [Magnussen], I knew he had a penalty and there was no need to attack him. It meant I could focus on keeping Jenson behind me, which was not easy.”
Perez moved ahead of Magnussen in the drivers' standings following Monza - 39 points to 38 - while Button jumped ahead of Perez's team mate Nico Hulkenberg, 72 points to 70.
In the constructors' championship meanwhile Force India gained one point on McLaren, meaning they are now just one point behind the Woking squad in the fight for fifth - the two teams sitting on 110 and 109 points respectively.