Hull had the best opportunities of a tight but poor-quality Premier League encounter at the KC Stadium and felt Jozy Altidore was denied a clear penalty in the second half after a tangle with Christopher Samba.
Blackburn had their opportunities, particularly after the introduction of the lively Nikola Kalinic, but had to settle for a point.
The result kept Rovers above Hull in the lower reaches of the table and both sides may see it as a wasted opportunity.
The match was billed as a battle between Brown and Rovers manager Allardyce, his former boss at Bolton.
Brown was visible throughout on the touchline but Allardyce, recovering from a recent heart operation, remained in the stands until the closing moments.