Connolly, 19, scored his first Premier League goal and Brighton's second on 32 minutes when he converted Dan Burn's cross at the second attempt.
The forward, making his first start in the Premier, claimed his second and put the match beyond doubt with a well-taken third and became the first Irish teenager to score a brace in the top flight since Robbie Keane did it for Coventry against Derby in August 1999.
“I can’t really describe it, I feel speechless," said Connolly. "I’ve been close to scoring in the last few matches but thankfully it’s come, and I’ve scored twice. It’s the proudest moment of my career so far and now I want to push on for more.
“It made it even more special that it was at the Amex; my dad flew over to watch in the hope that I’d start, and I looked up to celebrate with him when I got the second goal.
“I’m so grateful for the hard work all my family have put in and it’s great to know I’ve made them proud. They’ve dropped me to training and games when I was young, and sat out in the cold watching me, so that was for them today as much as it was for me.”
To complete a memorable day, the youngster from Galway was promptly called-up by Repubic of Ireland manager Mick McCarthy for their upcoming Euro 2020 qualifying double-header against Georgia in Tbilisi on 12 October and Switzerland in Geneva three days later.
"Aaron enjoyed his full debut for Brighton and we have been keeping a close eye on his progress this season," said McCarthy.