The defender netted an acrobatic strike from the edge of the box against Anderlecht, and the Rossoneri CEO struggled for superlatives to describe the effort
The France international brought down a cross with his back to goal before unleashing an spectacular effort past Silvio Proto from the edge of the box to double his side's lead midway through the second half.
"Mexes' goal was great, wonderful and one of the most beautiful of my 26-year reign, perhaps more beautiful than Marco van Basten's against Goteborg 20 years ago," the club's vice-president told Milan Channel.
The Rossoneri celebrate the 50th anniversary of their first European Cup success in May, and Galliani believes their place in the last 16 of this season's competition is important to preserve their reputation as one of the Continent's top clubs.
"With [coach Massimiliano] Allegri, we suffered a lot this summer and in the autumn, but this result is very, very important. It keeps us amongst Europe's elite.
"We are in the last 16 for the 10th time and have maintained our international ranking that distinguishes us from the rest by doing so.
"In May, we will celebrate 50 years since our first European Cup. We are the ones who have won the most international titles. That's something we must always remember.
"After being criticised for having an old squad, now we have a young team, it requires patience. Tonight we saw a 20-year-old [Mattia] De Sciglio pass the ball to a 20-year-old [Stephan] El Shaarawy for the first goal. I think it speaks volumes."
Meanwhile, Mexes downplayed the individual brilliance of his goal but was only happy to have played a significant role in helping the team progress to the knock-out stages of the Champions League.
"It was important to win," he told reporters. "We're pleased because we have met one of our objectives for the season, but now we are thinking about [next opponents] Juventus and the Scudetto.
"I dedicate my goal to my family. The win was important for a group of players that deserve more than what they have got so far.
"At half-time, the coach told us to be more aggressive and play nearer to our opponents' goal. We could've still done more."