Gary Bowyer's men started the day four points off the play-offs and rivals Reading, Brighton and Bournemouth all failed to win but they were frustrated by a dogged Yeovil side.
Jason Lowe struck a post early on and Jordan Rhodes forced a late save out of Marek Stech but it was a fruitless afternoon for the home side.
Yeovil had chances of their own, particularly in a spirited second half when Liam Davis fired wide and Joel Grant forced a save from Paul Robinson.
Rovers extended their unbeaten run to nine and remain four points outside the play-offs but the feeling around Ewood Park was of an opportunity missed.
Yeovil are running out of games and their survival hopes look remote. They are still bottom, five points from safety with three games remaining.
Blackburn were unchanged from the draw at Sheffield Wednesday but Glovers boss Gary Johnson had to do without the in-form Kieffer Moore for the trip to east Lancashire.
Lowe has scored once for Rovers previously and went agonisingly close to his second after four minutes when he was given time and space 25 yards out to rifle in a powerful low drive that cannoned back off the post.
They went close again soon after Craig Conway found space to whip in a deep cross but the prolific Rhodes headed wide at the far post.
The home side created all of the opening chances and Grant Hanley should have scored when he rose unchallenged but could only direct Conway's corner wide.
But the away side sprung into life after 23 minutes when Tommy Spurr's desperate intervention fell to Joe Ralls in the area who skewed his shot wide of the left post.
Yeovil were looking for a second away win in the space of three games and could have taken the lead after 56 minutes when Tom Lawrence drifted in from the left and set up Davis on the edge of the area but he fired wide.
Lawrence continued to cause Rovers problems and his 20-yard curling effort wrong-footed Robinson after taking a deflection but landed wide, much to the relief of the restless home faithful.
Yeovil substitute Grant almost made an immediate impact with 14 minutes remaining but his low shot was tipped wide by Robinson.
Blackburn rallied late on with Tom Cairney forcing a low save out of Stech and then the goalkeeper denied Rhodes who directed a header towards goal but the frustration was summed up with the boos at the end.