Last year's runners-up have not been beaten since Nov. 24 when they lost 3-1 to Ried.
Salzburg have now overhauled the previous record set by Rapid Vienna in 1987. The Bundesliga was launched in its current form in 1974.
Saturday's result was never in doubt after Brazilian Alan gave the home team an eighth-minute lead and the visitors had goalkeeper Szabolcs Safar sent off seven minutes later for denying a clear scoring opportunity.
Alan added another in the 24th minute, his 10th goal of the season, and Stefan Ilsanker and Sadio Mane made it 4-0 before halftime.
Dusan Svento and Jonathan Soriano, with his 12th goal of the season, completed the rout in the second half.
Salzburg have dominated Austrian football since they were taken over by the Red Bull energy drink manufacturers in 2005, winning the Bundesliga four times since then.
They have never qualified for the Champions League and angry fans founded a breakaway club, Austria Salzburg playing in their original violet and white, in protest at some of the changes introduced since the takeover.
Saturday's win left them eight points clear at the top with 28 points from 12 games.
Second-placed SV Groedig won 4-0 at bottom club Admira Wacker.
Admira, who have had eight points deducted for breaching licensing regulations, had two players sent off - Wilfried Domoraud in the first half and Andreas Leitner in the second.
Champions Austria Vienna drew 1-1 at Ried, leaving them fifth with 16 points.