Mac Allister struck the only goal of a keenly contested contest from the penalty spot in second half stoppage time after Luke Shaw was penalised for hand ball by the video assistant referee.
The win lifted Brighton into sixth position and they have games in hand on their rivals.
Roberto De Zerbi's side thus gained a measure of revenge after falling to the same side in the FA Cup semi-finals eleven days prior.
World Cup winner Mac Allister was delighted with the win and wants his teammates to continue their pursuit of continental football next season.
“We know that it’s the end of the season and these three points are very important,” he told Brighton’s club website.
“The way we are playing is very important because we feel very good. We will do our best to finish as high as we can.
“We have to think about ourselves and not look at the other teams. If we play the way we play, we will have big chances to fight for a European spot and that has to be our aim.”
“It was so special,” he added. “For the team and the fans, it was an amazing win and something unforgettable.”
Brighton are back in action with another home game against Everton next Monday.
