Yepremian's wife, Maritza, said he died at a hospital in Media, Pa. His illness was diagnosed in May 2014, she said.
Yepremian played from 1966 to 1981. A son of Armenian parents, Yepremian was born in Cyprus and came to the United States at age 22 and kicked in the first NFL game he ever saw.
"Garo was one of the most popular and productive players in Miami Dolphins history, and we were sorry to learn of his passing. His effusive personality supplemented his strong competitive nature, and no one made more pressure kicks than Garo," the Dolphins said in a statement.
His 37-yard field goal in the second overtime ended the longest game in NFL history, a Dolphins' playoff victory over Kansas City on Christmas 1971, and he helped Miami win back-to-back NFL titles in 1972-73. But Yepremian's gaffe in the fourth quarter of the Super Bowl in January 1973 nearly spoiled the Dolphins' bid to complete a perfect season.
With Miami leading 14-0 and on the verge of finishing the season 17-0, the Washington Redskins blocked Yepremian's field-goal attempt. He picked up the ball and tried to throw it but fumbled, and the Redskins' Mike Bass ran it 49 yards for a touchdown.
"Every airport you go to, people point to you and say, 'Here's the guy who screwed up in the Super Bowl,'" Yepremian said in a 2007 interview. "After a while it bothers you. If it was anybody else he would go crazy, but fortunately I'm a happy-go-lucky guy."
"I thought, 'Boy, this will be great if Garo kicks this field goal and we go ahead 17-0 in a 17-0 season. What a great way that would be to remember the game,'" Shula said. "And then Garo did what he did, and it's 14-7 with still a couple of minutes to go. I'm looking for Garo, and I'm ready to kill Garo, and I couldn't find him. He went down to one end of the bench, and I haven't seen him since."
In a statement Saturday, Shula said: "When you think back about Garo there were a lot of great moments and some that were not so great. No matter what, though, he had a positive attitude all the time. He always wanted to be involved in everything and I enjoyed having him on the team. He was unique in Dolphins history and will be missed."
Despite Yepremian's mistake, Miami won to complete the NFL's only perfect season. Yepremian also kicked for the Dolphins when they repeated as champions in 1973. Prematurely bald and only 5-foot-8, the left-legged Yepremian hardly looked like an NFL star.
"Being as small as he was, I didn't know how he kicked a ball so far and so straight, but he did and made most of his field goals. He was a huge part of the success of those great teams," said Dolphins great Bob Griese.
Yepremian broke in with the Detroit Lions, who signed him as their first soccer-style kicker when that approach was a novelty. As a rookie in 1966 he broke a league record with six field goals in a game at Minnesota. He joined the Dolphins in 1970, made the Pro Bowl twice with them and led the league in field-goal accuracy three times. He also kicked for the New Orleans Saints and Tampa Bay Buccaneers.
Private funeral arrangements are pending. A viewing is planned Wednesday in Wynnewood, Pa.
The Associated Press contributed to this report.