Madden gave the Glovers the perfect start in the eighth minute. James McAllister whipped in a free-kick from the right and Madden, on loan from Carlise, was left totally unmarked to head in at the far post.
Had it not been for a fine save from former Yeovil goalkeeper Chris Weale to push away a sweetly struck 25-yard drive from Keanu Marsh-Brown, Gary Johnson's men would have been further in front by the break.
A tepid Shrewsbury side, missing suspended top scorer Marvin Morgan, carried little threat with their only meaningful chance in the first period falling the way of Asa Hall, who nodded a Paul Parry cross over the bar.
Yeovil doubled their advantage in the 59th minute when Marsh-Brown easily beat Joe Jacobson and crossed for James Hayter to touch home. And it got even better for the visitors in the 71st minute when Ed Upson's deep cross was headed in by Madden, hardly believing his good fortune.
Shrewsbury struggled throughout and their only bright spot came 10 minutes from time when Matt Richards stroked home a penalty after Tom Bradshaw was barged over by Daniel Johnson.