The title capped a roller-coaster first season for Beasley at Rangers. He was sidelined with a knee injury suffered playing in a European Champions League match against Stuttgart.
Beasley gave Rangers a 2-0 lead in the 43rd minute when his corner to the far post was headed back across goal by Carlos Cuellar to Beasley, who scored from 12 yards.
After second-level Queen of the South tied the score, Kris Boyd scored his second goal of the game on a header off a Beasley corner for the winning goal in the 72nd minute.
"To score, and to be on the winning side, made it quite a day," Beasley told the Independent from the U.S. camp outside London, where it is preparing for Wednesday's game against England. "And it was my birthday, too."
The victory meant Rangers completed a cup double. It won the Scottish League Cup in March. The win over Queen of the South was also consolation for Rangers having lost in the UEFA Cup final to Zenit St. Petersburg 10 days earlier and finished second to Celtic in the Scottish Premier League, whose race ended only two days earlier.