The Glovers' biggest home defeat in the Football League was inevitable when an already-weakened team had midfielder Michael Woods sent off in the 33rd minute for a foul.
They were 1-0 down at the time, and never looked capable of drawing level.
Luke Freeman, a one-time Yeovil loanee, gave Boro the lead on 14 minutes, and Patrick Agyemang added a second just before the break.
The second half was all Stevenage. Jon Ashton got the third with a simple header from a corner, and Yeovil's defence fell apart conceding goals from crosses.
Freeman set up two for Jamaal Lascelles (71) and Mark Roberts (82) and then completed the scoring himself with a tap-in two minutes from time.