It was the Fight of the Century. On March 8, 1971, Muhammad Ali and Joe Frazier stepped into the ring at Madison Square Garden to battle for the title of Undisputed Heavyweight Champion of the world—and a then-record $2.5 million purse.

In honor of the match's 40th anniversary, LIFE has published a series of never-before-seen images taken by staff photographer John Shearer. The three that appear below document the progression of the fight: First, the press' infatuation with the charismatic presumed winner, Ali; second, Ali's flagging energy midway through the bout; and finally, Frazier's quiet satisfaction at beating Ali by unanimous decision in 15 rounds.

mega_watermark_ugc1179671_slide.jpg

Muhammad Ali, pre-fight weigh-in, March 1971

mega_watermark_ugc1179841_post.jpg

Between rounds at Madison Square Garden, March 8, 1971

mega_watermark_ugc1179861_post.jpg

Joe Frazier in his dressing room after the fight

See the full gallery at LIFE.com.

Image credit: John Shearer/TIME & LIFE Pictures/LIFE.com

We want to hear what you think about this article. Submit a letter to the editor or write to letters@theatlantic.com.