The shorts they wore truly were short. When their NBA teams traveled to distant cities, the players picked up their bags at the airport carousel themselves. They had roommates. The reporters who covered them smoked, and when they worried about finding the Western Union office to send their stories back to their newspapers, they consulted a phone book.

It was 1969, otherwise remembered for Richard Nixon’s inauguration, Neil Armstrong’s one small step, and the introduction of the Pontiac Firebird Trans Am. At the time, Leigh Montville was roughly a year into his stint as a sportswriter at the Boston Evening Globe; in that endeavor he was armed with a Olivetti Lettera 32 in a baby-blue case. (Note to readers: The Olivetti was a portable typewriter, the favored tool of the journalism set; as for evening newspapers, they sank like a Steph Curry free throw, without the grace.)

Mr. Montville’s assignment was to cover the NBA championship series between the Los Angeles Lakers and the Boston Celtics, a clash of two great teams, of course, but a cultural clash too, not just buttoned-up New England against free-thinking California but also Wilt vs. Russell: the Lakers’ Wilt Chamberlain and the Celtics’ Bill Russell. Older basketball fans might say—with apologies to four other one-name boldface names—Magic, LeBron, Michael and Kareem—that we have never seen their like again.

The championship series, Mr. Montville tells us in “Tall Men, Short Shorts,” was full of “melodrama, suspense, transcontinental electricity.” Chamberlain and Russell were accompanied by a supporting chorus of hardcourt virtuosos: Jerry West and Elgin Baylor for the Lakers; John Havlicek, Sam Jones and Tom Sanders for the Celtics. This was the sixth time the Los Angeles Lakers had faced the Celtics for the NBA crown. After five losses, the Lakers were hoping for redemption, but the Celtics had won 10 championships in the past 12 years. As the poet Seamus Heaney might have said if he were one of the habitués of the old Boston Garden: Hope and Celtic history had a beguiling way of rhyming.

Mr. Montville’s chronicle—both reported and reflective—is part memoir, part sports story. At the time, he was just 25, making a salary of $11,055. (Wilt made $225,000 that year.) Now, at 77, he is looking back. Back to an era when the knights of the keyboard, as Ted Williams called his cursed chroniclers, supped, but mostly drank, at Toots Shor’s restaurant at 51 West 51st Street in New York. Back to an era when Mr. Montville and his posse were garbed in “$40 sports coats, khaki trousers, and Bass Weejun loafers in need of a shine.” Back to an era when “Hair” was on Broadway (and Jupiter aligned with Mars) and when women’s basketball was played with six players (in jumpers) on a side.

There was an innocence to the NBA in the 1960s, or so it now seems. It lacked three-point shots, cable commentary, and the blaring of “We Will Rock You” or, heaven forbid, “We Are the Champions,” which would have been a bit much at the old train barn at 150 Causeway St. where the Celtics played. Team practices were intense but without show-biz drama. “This,” Mr. Montville says of one such session, “could be a basketball practice at the local YMCA, youngish accountants and plumbers, bartenders and schoolteachers, getting ready in obscurity for the Men’s League finals.”

Not so the games. As for the championship series, the Celtic dynasty seemed to be endangered, almost certainly to be upended by Wilt and the stalwarts of the rising West. It was a contest, Mr. Montville says, between “the stardust Lakers” and “the decaying Celtics.”

At the center, on the court and in other ways as well, was Russell—gifted, proud, enraged at the injustice he saw and experienced in a city that regarded itself as the cradle of liberty. “Russell decided, early in his career,” Mr. Montville writes, “that he played for the Celtics. He played for his teammates. He played for his coach. He did not play for the city of Boston.” Off the court but not off the record, Russell was an activist. As for Chamberlain, he was a Richard Nixon guy. His mode was less militant than on the make. He may have been known since his youth as “the Big Dipper,” but in maturity he was a shooting star only when he was in close orbit to the basket.

The two centers may have been friends, or at least friendly—they once had Thanksgiving dinner together—but they had different temperaments, different approaches to the game. “If Russell’s team won, it was a triumph of the spirit, a mixture of cunning, planning, and hard work,” Mr. Montville writes. “If Chamberlain’s team won, it was a show of force, talent, brute power. The theatrics, either way, were wonderful.”

Mr. Montville takes us through all seven games in a pastiche of newspaper stories, radio accounts and his own reminiscences. It is all remarkably engaging, considering that the series took place more than 50 years ago, but it is a 10-page examination of a 6-second play in Game 4, at Boston Garden, that gives the book the feel of a classic.

The moves in the Celtics’ “secret play”—one that Havlicek and point guard Larry Siegfried had used at Ohio State and that the Celtics had practiced only a few weeks earlier but never employed—somehow got the ball to Sam Jones, who, off-balance, somehow lifted his shot into the air, and the ball, spinning off the front rim to the back rim, somehow—do you believe in miracles?—fell into the basket with just one second remaining, allowing the Celtics to tie the series at 2-2 with an improbable 89-88 win. “The play sounded as if it had been sketched out in the dirt in the second half of a schoolyard touch football game,” Mr. Montville writes. “You go here. You go there. You and you go there and there. Sam, you get the ball behind the triple pick and take your favorite jump shot.”

Many fans heard the end of this titanic struggle on the radio because the Red Sox-Yankee game that night had ended after two hours and 14 minutes of play. Yes, really. These days, two hours and 14 minutes of baseball will get you into the sixth inning, maybe. Now you know why the NBA may have a brighter future than MLB.

It is true that “Tall Men, Short Shorts” has a Boston orientation. But Mr. Montville makes brave tries at balance. Here, for example, is his assessment of Jerry West, remembered today for his profile, almost like a 19th-century daguerreotype, on the NBA logo: “He was everything the good folk of Los Angeles wanted, a basketball version of Sandy Koufax, Cary Grant in sneakers, almost elegant in the way he played the game.”

Even so, the Boston characterizations have more zip, possessing almost a cinéma vérité quality. Mr. Montville’s portrait of Red Auerbach, who at the time was the Celtic general manager, includes this: “Sitting on the visitor’s side of Auerbach’s overrun desk was like visiting some insurance agent who had been in business a very long time, some accountant who smoked his cigar and dropped ashes on your return while he talked about a world problem or an undeserved parking ticket just yesterday.”

Oh, one more thing. The Celtics won the series in the seventh game. But, truly, that is the least of the matter.

—Mr. Shribman, a former Journal political reporter, teaches at the Max Bell School of Public Policy at Montreal’s McGill University.