The Washington Capitols and the Houston Rockets won their opening 15 games in 1949 and 1994 respectively, and the Golden State Warriors won their first 24 in 2016.
All three reached the NBA Finals, although the Rockets were the only team to win the championship.
“Everyone is showing tons of energy, all over the city,” Allen said.
“It’s incredible how Cleveland has adopted us. They come to every game, yelling for everything. The city of Cleveland has our backs.”
The Cavaliers, who are top of the Eastern Conference, travel to second-placed Boston Celtics, the defending NBA champions, on Tuesday.