Julio Enciso, Deniz Undav and Pervis Estupinan were all on target in the second half as Brighton moved into sixth place with the win while also virtually ending Arsenal's title hopes.
Brighton have 58 points from 34 games and two wins from their final four games would guarantee them a place in Europe next season, most probably in the Europa League.
"I'm really pleased with the performance but the season is not finished for us," Italian De Zerbi, who took charge when Graham Potter left for Chelsea in September, said.
"The 58 points on the table we have are not enough, we are fighting for a big, big target so we have to win more games."
Brighton bounced back from a surprise heavy defeat at home to Everton with a clinical display at Arsenal to move above Aston Villa and Tottenham Hotspur in the race for Europe.
But while they have games in hand over the teams around them, they have some tough fixtures with Manchester City and Newcastle United and Aston Villa all still to play, although they also have a home game against relegated Southampton.
"It had been a very tough week after Monday's result, but today we showed character and passion, we showed we are serious people," De Zerbi said. "I have to repeat, I am lucky to be the coach of Brighton. I have a lot of great players.
"We have to improve our mentality so we give our best in every game and every training session, and we have to adapt to playing many games in a row but we are a great team."
