Arsenal were forced to play around half an hour with 10 men but hung on to in Monday's 1-0 win at Crystal Palace.
Defender Takehiro Tomiyasu was sent off for a pull of Jordan Ayew's shirt in the 67th minute. He had also received a yellow for time wasting earlier in the second half.
Due to the intense ending to the match, Arsenal celebrated like they had won the title after the final whistle.
"It shows how much we want it," Arsenal coach Mikel Arteta said of the celebrations.
"When you see the players on the bench ... they have to come and help the team. They were magnificent and they changed the dynamic of the game. I say thank you so much to them because they really contributed to winning the game," he added.
Arteta said it would take some time for teams to adjust to the strict time-wasting regulations that has led to more yellow cards and additional time being added on at the end of each half.
"It's going to be very difficult for us. I guarantee you, we will have to play with 10 or maybe with nine or with eight depending where we put the standards and the level. We can play eight against eight, it can be very entertaining," the 41-year-old said.
Arteta’s Palace counterpart Roy Hodgson, who has dealt with a lot of changes over the course of his 50-year managerial career, also shared his opinion on the new laws.
"These rules and these ideas are thrust upon us, we don't have too much say in the matter, but we have to learn to live with them," he told Sky Sports.
The only goal of the match was scored by Martin Ødegaard after he converted a penalty in the 54th minute.
Arsenal have won both their games in the new Premier League season, so far, and are currently on third position on the table.