Pep Guardiola's side rub shoulders with the famous Real Madrid team which included Alfredo di Stefano, who had helped them to win the first five European Cups between 1956 and 1960.
"It's an immense honour to have 15 consecutive victories and to equal the record achieved by the Real Madrid of Di Stefano," Barca coach Pep Guardiola told reporters.
"I am sure some team will equal it or pass it one day but it is something no one has managed for 50 years."
Barca started their run with a 2-1 victory at home to Valencia on October 16 and have gone on to rattle in 57 goals while conceding only six in their 15 matches.
Their closest rivals in the league, arch-rivals Real, were hammered 5-0 at the Nou Camp in November, and third-placed Villarreal fell 3-1.
They pass the club record of 14 wins set by Frank Rijkaard's team in the 2005-6 season which went on to win a La Liga and Champions League double.
The champions have a King's Cup semi-final second leg away to Almeria on Wednesday when they defend a 5-0 advantage, and then have the chance to set a new La Liga win record at home to Atletico Madrid next weekend.
