The 17-year-old came off the bench to claim the only goal of the game in the 92nd minute to seal the three points in the Scottish Third Division clash.
The win was Rangers' tenth in a row and allowed them to stretch their lead at the summit to 15 points, as they seek to wrap up the title as soon as possible.
Aird said: "It was my first goal for the senior team and nothing can compare to that goal.
"To be honest, I thought I took my touch too far. All I saw was the post and I just curled it and it happened to go in.
"It was a dream come true. It was unbelievable, one of the best feelings of my life.
"I'd say it was better than my debut to be honest."
The teenager has been battling to force his way back into the side after recovering from a fractured thumb and hopes he has done enough to impress the manager.
He added: "The gaffer told me to go on and just do the best I could and I think I did that.
"I've been trying to get back into the team for the last couple of weeks and hopefully I can get my spot back in the team.
"I thought I came on and did quite well."
The last time Rangers played at the national stadium, they defeated Celtic to clinch the Scottish Communities League Cup in March 2011.
This time around, a crowd of 30,117 watched an alternative Glasgow derby in Scottish football's bottom tier.
Aird said: "It was a big day for the club, bringing that many fans to Hampden.
"We usually only come here when it's cup finals so it was quite weird coming here for a league game.
"It was good and I'm sure the fans really enjoyed it. Getting the three points for the team pleases me even more."
He added: "All the family were back home in Toronto watching the game.
"My dad has actually been sick for the last couple of games but I told him I was on the bench so I'm sure he got out of his bed.
"He'll be glad that he did."