Liverpool generated a chance after three minutes following a free kick, but Luis Suarez's shot flew high.
Christopher Samba succeeded in scuppering a number of the Reds' chances during the first session, while goalkeeper Mark Bunn - in for injured Paul Robinson - proved himself against a number of shots from Charlie Adam.
Liverpool thought that they had opened scoring on the half hour mark, but Andy Carroll's goal was disallowed when a touch on from Suarez was deemed to be offside. Meanwhile, the home side were disappointed to not receive a penalty following Bunn's challenge on Maxi Rodriguez.
While Blackburn - fielding Yakubu as a lone striker - had a paucity of chances in the first half, they received the first entry on the scoresheet on the cusp of half time when Adam put through his own net from a fumbled challenge on Mauro Formica.
The second half saw an early comeback from Liverpool as they attacked with increased vigour and afforded their guests little possession. A chance was finally converted eight minutes after the break when Maxi headed in from a Martin Skrtel cross.
While Liverpool succeeded in keeping play in the away side's half for much of the second period, Bunn continued to foil a barrage of shots.
Blackburn's point leaves them at the bottom of the Premier League table, while Liverpool are in sixth.