1971–72 season

The Braves repeated their 22–60 record in the 1971–72 season, but did make good acquisitions that would make the club better. Buffalo drafted center Elmore Smith from Kentucky State University and local favorite Randy Smith from Buffalo State College. Johnny McCarthy replaced Schayes one game into the season as the team's head coach.

1972–73 & 1973–74 seasons

Ernie DiGregorio was named NBA Rookie of the Year in 1973–74 after leading the NBA in assists and free throw percentage.

The team did slightly worse in the 1972–73 season, as it went 21–61 under new head coach Dr. Jack Ramsay. In a showcase of the futility of the '72-'73 Braves, during the team's fifth game of the season on October 20, 1972 the team set an NBA record which still stands for most points in a single quarter with 58 in the fourth quarter against the Boston Celtics. However the Celtics were in the process of a blowout win and had already lead the Braves 103-60 at the start of the quarter. They had inserted their substitutes to play the final quarter and the reduced quality of the opponents allowed for the comeback. The Braves outscored the Celtics 58-23 but still lost 126-118. The Braves' big move that season was drafting forward/center Bob McAdoo from North Carolina. The team finally made its first playoff appearance in 1974, in which they faced the Celtics and lost in six games. That season, McAdoo posted averages of 30.6 points and 15.1 rebounds; this is the last time any player has averaged at least 30 points and 15 rebounds in the same NBA season. Also, that season, the Braves rookie Ernie DiGregorio won the NBA Rookie of the Year Award.

1974–75 & 1975–76 seasons

Bob McAdoo (11) was the NBA MVP in the 1974–75 season after averaging 34.5 points per game and 14.1 rebounds per game.

In 1974–75, McAdoo was awarded the NBA Most Valuable Player Award, averaging 34.5 points, 14.1 rebounds. and 2.12 blocks per game, while shooting 51.2% from the field and 80.5% from the free-throw line. The Braves made trips to the playoffs in both 1974–75 and 1975–76, the latter of which would be their last playoff berth playing in Buffalo.

1976–77 season

The Braves by this point were a modest success, both on the court and off; the team was drawing close to the league average in fans, had solid broadcasting ratings and was turning a consistent profit. Even so, by 1976 Snyder was facing severe pressure to sell the team and get it out of Buffalo. As a result of the Braves only getting the third choice of dates at the Aud, the entire NBA was unable to finalize a schedule and hammer out television contracts until the Sabres and Griffins finalized their schedules. The NBA considered this untenable, and gave Snyder five years to resolve the problem. In a 2016 interview with The Buffalo News as part of a retrospective on the Braves, Snyder laid particular blame on Canisius president Father James Demske for making it difficult to get good home dates at the Aud. Snyder recalled offering Demske $125,000 per game to give up some Saturday night dates to the Braves. However, Demske turned the offer down, believing that the Braves posed a threat to the Little Three rivalry in college basketball. When the five-year deadline expired without a resolution, Snyder found himself with two options–build a new arena or sell the team. Building a new arena wasn't financially realistic at the time, leaving Snyder with no option but to sell the team. Had the dispute been resolved, the Braves would have likely been able to stay in Buffalo, especially since Canisius basketball went into what would be permanent decline in the early 1980s.^[4]

At the time, Snyder's more public feuds were with the Sabres, whose owners, Northrup and Seymour Knox, represented Buffalo's old money circuit while Snyder had nouveau riche status. Years later, Snyder attributed these feuds to his own inexperience with sports ownership and now speaks in more conciliatory tones regarding his hockey competition.^[7]

The June 15, 1976 issue of Buffalo's Courier-Express blasted the headline "Braves Go to Florida, Leaving 'Hockey Town'". Snyder had a handshake deal to sell the team for $6.1 million to hotel owner Irving Cowan, who would move the Braves to the Hollywood Sportatorium outside of Miami, Florida. However, the city of Buffalo filed a $10 million damage suit to block the move. The sale eventually fell through and the Braves and the city signed a new 15-year Memorial Auditorium lease in July with a provision that the lease could be voided if the team did not sell 5,000 season tickets in any season. Later that summer, Snyder finally sold 50% of the franchise to businessman John Y. Brown Jr., who had previously owned the Kentucky Colonels of the American Basketball Association (ABA). Brown later acquired the remaining half from Snyder sometime in the 1976–77 season and resold that share to another businessman, Harry T. Mangurian Jr.

Brown and Mangurian proceeded to dismantle the Braves. Ramsay, unwilling to have his career hurt by the change in ownership, left for the Portland Trail Blazers, who would win the NBA championship in the upcoming 1976–77 season.^[8] A provision in the team sale agreement stipulated that if Brown sold the contract of any Braves player, then the money would go to Snyder and the purchase price would be reduced. This subsequently occurred when the Braves sent McAdoo to the New York Knicks for players and cash midway through the season. Before the first game of the season, the Braves also managed to acquire eventual Hall-of-Fame center Moses Malone from Portland. However, after just two games in which he played a total of six minutes, he too was traded; he was sent to Houston for two draft picks. He would finish the season in Houston averaging 13 points and 13 rebounds while only two years later winning his first of three MVP Awards. The Braves would go through four head coaches in the next two seasons: Tates Locke, Bob MacKinnon, Joe Mullaney (formerly coach of the Colonels) and Cotton Fitzsimmons.

1977–78 season

The team's poor play in its final two years (30–52 in 1976–77 and 27–55 in 1977–78) and the overt attempts to break the lease on Memorial Auditorium drove attendance down below the threshold that would have been needed to break the lease.^[4] John Y. Brown met with Irv Levin, who then owned the Celtics, and negotiated a deal in which the owners would swap franchises, with Brown taking control of the Celtics and Levin getting the Braves. Levin was a California businessman, and wanted to own an NBA team in his native state. However, he knew the NBA would not even consider letting him move the Celtics. He was therefore very receptive to Brown's offer. The deal was brokered by then NBA general counsel David Stern, who became the league's commissioner in 1984. Following what would be the Braves' final season in Western New York, the NBA owners voted 21–1 to let the team move. As Levin wanted, he became owner of a team in San Diego after the 1977–78 season, which became the San Diego (now Los Angeles) Clippers.^[9][10] As part of the transaction, the teams traded most of the players on their rosters.^[10]