An early James Hayter penalty and a stunning solo effort by Paddy Madden saw off the Shropshire side to further boost the Glovers' play-off ambitions.
The visitors, who came into the game unbeaten in their last four matches, started brightly with Tom Eaves and Jon Taylor both spurning early openings.
But Yeovil - who have lost only one of their last 13 matches at Huish Park - hit back and took the lead when Hayter converted from the spot after Marvin Morgan was penalised for handball.
The Shrews soon equalised after Joe Jacobson's fizzing cross found the onrushing Stephen McGinn, who lashed home from the edge of the box.
Just after the half hour, League One's leading marksman Madden restored the hosts' advantage with a scintillating strike to notch his 23rd goal of the season.
Yeovil survived a second half onslaught with Shrewsbury captain Matt Richards almost drawing his side level with a curling effort before Eaves fired wide and McGinn was denied by Marek Stech.
But Gary Johnson's men held on to claim three precious points.