Six teams since 1983 have outrebounded their opponents at least 15 regular season games in a row.
The Cleveland Cavaliers did it from Dec. 2007 to Jan. 2008, winning 12 out of 15 games. That year the team surrounded Lebron James with many great rebounders, including Zydrunas Ilgauskas, Drew Gooden, Anderson Varejao, and Ben Wallace. During the streak they outrebounded their opponents 48.0 to 39.5.
The New Jersey Nets and Chicago Bulls both did it for 15 games during 1997, two teams at the opposite end of the spectrum. The Nets won only 6 of the 15 games spanning two seasons. Strangely, the streak began after the Nets lost their best rebounder, Jayson Williams, to injury. Eric Montross and Tony Massenburg stepped up and each averaged over 10 rebounds a game in his absence.
As for the Bulls, they won 13 of 15 games in the streak, on their way to the NBA Championship. They outrebounded their opponents by over 10 a game, 48.8 to 37.7. Dennis Rodman was the key to this streak, fetching over 14 rebounds a game.
The Utah Jazz have had two streaks of 16 games outrebounding their opponents – with two very different teams. The first time was in 2002, with a team led in rebounding by a 38-year old Karl Malone. This was not an exceptional rebounding team, only outrebounding their opponents by 4 a game over the season. They won 8 of the 16 games.
The 2015 Utah Jazz team traded away Enes Kanter at the All-Star break, leaving space for Rudy Gobert to begin starting for the team. After the trade, they outrebounded their opponents by almost 7 rebounds a game, with Gobert averaging over 13 rebounds per game. This trade turned the season around for the Jazz, as they won 13 of the 16 games in the streak after starting the year 19-34.
But the best streak of all time belongs to one of the best teams of all time, the 1985-86 Boston Celtics. They had a streak of 17 straight games outrebounding their opponents, winning 13 of them. The team was lead, of course, by the talented trio of Bird, Parish and McHale, and went on to win the NBA Championship that year.