In 1961, during spring training in Florida, LIFE gave 25-year-old Yankee shortstop Tony Kubek a camera and asked him to photograph his teammates: Mantle, Berra, Maris, Ford, and the rest of the players on what would be seen, in time, as one of the greatest teams in baseball history.

The resulting photos were never published. (See slide 12 in this gallery for a possible reason why.) Now, five decades later, LIFE.com presents those pictures, along with Kubek’s own insights and memories of that particular spring training, and that singular, unforgettable era of pro ball.

Kubek, the 1957 American league Rookie of the Year, played his entire nine-year career with the Yankees, winning seven American League pennants and three World Series. After he retired, he embarked on a distinguished broadcast career, working for NBC for more than 20 years (as an analyst for the network’s Saturday “Game of the Week,” among others) and calling Yankee games for the MSG network for another five. In 2009 he was given the Hall of Fame’s Ford Frick Award, bestowed on a broadcaster for “major contributions to baseball.” Now 76 years old, he lives in Wisconsin. He doesn’t follow pro ball much anymore. (He retired from broadcasting in 1994, he says, because “I got tired of hearing myself talk, and it was time to get on with another phase of life with my wife, Margaret.”) But the images in this gallery obviously had some resonance for him, and after all these years, they got him talking again — about his own playing days; about the game as he knew it back then; and about guys with names like Mickey, Yogi, Elston, Whitey, Moose, Bobby, Roger — his teammates, and his friends.

On Mickey Mantle:

“One amazing thing about Mickey,” Kubek told LIFE.com, “is what he was able to accomplish despite the devastating injuries he suffered. [Note: Mantle suffered serious damage to his legs starting in his teenage years, and played through pain his entire pro career.] This has all been well-documented, of course, but as his teammates we saw it, every day — how he had to tape his legs with huge Ace bandages before every game, from hip to ankle, and then he’d go out and somehow run down a shot to deep center field that no one else would have been able to catch, or he’d hit one of his huge tape-measure home runs. He did all that for years and years on legs that, after a game, were so swollen and in pain that we would have to physically help him out of a cab, because his knees wouldn’t hold his weight.” In 1961, bad knees and all, Mantle hit .317, drove in 128 runs, and (famously, in his race after Babe Ruth’s home run record with teammate Roger Maris) hit 54 homers.

On Roger Maris:

Kubek recalls Maris as one of the greatest multi-tool ballplayers he ever saw. “For a few years there,” Kubek says, “Roger was as good an all-around player as there was in either league — and I’m including Willie Mays and Hank Aaron and all the other Hall of Famers from that era. He could run like hell, he had an arm like a cannon — and could throw with accuracy — and of course he was a tremendous hitter. The best thing and the worst thing that ever happened to Roger was hitting those 61 home runs in 1961, because it distracted from what a complete baseball player he truly was.”

On Bobby Richardson:

“I roomed with Bobby for years,” Kubek recalls, “and beyond his remaining a good friend, let me tell you, he is highly underrated as a player. People say, ‘Well, sure, he was the World Series MVP in 1960 [He remains the only player from a losing team ever to win the award; Richardson hit .367 and drove in 12 runs in the seven-game loss to the Pirates.] but that’s about all they know of the guy. But he was an All-Star, he won a lot of Gold Gloves, he was solid at the plate. Bobby was a damn good ballplayer, and a central part of that team in 1961.”

On Elston Howard:

“Ellie should be in the Hall of Fame,” Kubek says, simply and firmly, of his old teammate, the first African American to play on the Yankees. “Elston not only starred in the Negro Leagues, but he then went on and played in the majors for years. He was an All-Star, won world championships, won Gold Gloves, was a league MVP — he was Hall of Fame caliber.”

On Bob Turley:

Turley was no slouch on the mound (he won a Cy Young Award and a World Series MVP award during his career), but 1961 was almost a lost season for him. “Bob had an injured arm and was close to going home because he felt like he couldn’t help the team and maybe should make room for another, healthier player,” Kubek told LIFE.com. “But the reason Turley stayed for the year, even if he was on the bench for much of it, is that [new Yankee manager Ralph Houk] said, ‘Bob, you’re not leaving.’ Now, here’s the thing. Bob, who later became a pitching coach himself, had an amazing knack where he could look at a pitcher and — simply by studying the way the guy held the ball or moved his glove or stood on the mound — he could call the pitches. He knew what was coming!”

On Whitey Ford:

“Despite Mickey hitting 54 home runs and Roger’s 61, and all the other guys hitting pretty well, we didn’t lead the league in scoring in 1961,” Kubek points out. “The fact is, what won us the pennant was Whitey Ford. Ralph Houk and Johnny Sain decided that he would pitch every fourth day, and he ended up winning the Cy Young, with a 25-4 record. Elston Howard called him the Chairman of the Board, and in 1961 — when we were coming off that crushing loss to the Pirates in the 1960 Series — that’s exactly what he was. Whitey was the real deal.”

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NOTE: Another version of this gallery appeared, in different form, on an earlier incarnation of LIFE.com.