The Bees led after 15 minutes when Maupay turned home a rebound before the French striker became public enemy No1 with the Spurs faithful as he wound up several home players and got booked for a clash with Dejan Kulusevski.
Shortly after scoring, Maddison and Maupay were spotted by TV cameras tersely exchanging words as the Bees goalscorer grimaced and patted his opponent on the chest.
However, Tottenham had the last laugh with three second-half goals earning a 3-2 win, which featured a nervy finish after Ivan Toney scored in the final half hour.
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Destiny Udogie levelled up after the break before Brennan Johnson fired home 73 seconds later, and the Welshman pulled out the darts move himself in celebration.
Spurs had the last laugh when Richarlison scored their third and also replicated Maddison's trademark celebration, and the midfielder explained his exchange with Maupay after the final whistle.
Maddison told TNT Sports: "I just said that he probably hasn't scored enough goals of his own to have his own celebration, so he had to steal mine."
In an Instagram post, Maupay wrote: "Went a bit early with that one. Gutted we couldn’t get the win. More goals and less relegations in my career than James Maddison. We go again Monday."
The game marked Maddison's first start since November after a long spell out with an ankle injury.
He added: "It's lovely to be back, when you're starved doing what you love, that reminded me why I love football. The first-half was stop-start, a lot of stoppages, which is how they have been successful, second half we created a lot of chances, scored some goals, but it's never simple - there's always a lot of goals at the Tottenham Hotspur Stadium.
"My Mrs will say I'm a moaner at the best of times, so it's tough. The design at Spurs, the treatment tables are in front of the pitches, it's tough. But I'm through it now, you've got to take the positives."
Johnson scoring the second goal provided another comeback narrative for Tottenham after two-and-a-half months since he last found the back of the net.
He stated: "It was a weird game, we expected what was going to come, for them to get set pieces and play a tough game and we fell for it in the first half. We were getting riled up by some of their players. Second half, we just had to take a deep breath and play our football.
"It was one of those games, the manager said it: once we score one, we will score two and three. Those were his exact words. As soon as we scored that first goal so early, we had to keep that momentum going.
"I knew I had to be there for my goal because that's what the manager demands from our wingers, to get to the back-post and when I got there I was happy. Recently, it's no secret, I haven't been at my best and in those sort of situations I haven't been in the right positions, so today I had to be.
"They are a really hard working team and I have noticed it for a long time, they're always in games. Even if they come here and concede three goals, they scored a second goal and made it hard for us at the end."