Veteran striker James Hayter netted twice whilst Joel Grant and Kieffer Moore made sure of the victory as Russell Slade's injury-hit Orient could not mirror their impressive league form against Championship opposition.
The relentless rain which engulfed the south west throughout the week left a heavy Huish Park pitch which resulted in both sides taking the first 10 minutes to adjust to the conditions.
Orient were perhaps better to get to grips with the sticky surface with Dean Cox having a goal-bound effort deflected away from danger early on, which was followed by a flurry of corners.
However, Yeovil took the lead after 12 minutes when Shane Duffy beat O's goalkeeper Jake Larkins to Luke Ayling's free-kick allowing Hayter to head into the empty net from close range to give the hosts an early lead.
Yeovil's opening goal took the sting out of Orient's early vigour and the Glovers almost doubled their lead with 10 first-half minutes remaining when Hayter engineered space well before dragging an effort wide of the target from inside the box.
Larkins, making just his fourth professional appearance, was saved from embarrassment when his clearance which was charged down by Sam Foley trickled out for a goal kick as Gary Johnson's side went into the break a goal to the good.
The Glovers dominance continued after the break and their lead was doubled after 49 minutes when Liam Davis' precisely placed cross to the back post was guided home by the lively Grant as Yeovil looked to take control.
Orient continued to persevere with their patient build-up play, but found themselves 3-0 down on the hour mark.
Kevin Dawson jinked past Gary Sawyer down the right flank before delivering a cross onto the head of the unmarked Hayter who grabbed his second of the match by glancing a header past Larkins from 12 yards.
Both sides emptied their substitutes benches with the result seemingly settled and O's striker Shaquile Coulthirst almost grabbed a consolation but his effort was saved by the legs of Marek Stech with a little under 10 minutes remaining.
Yeovil continued to press for a fourth goal, though, and were rewarded in second-half stoppage time when replacement Moore coolly slotted past Larkins to put the gloss on an impressive victory.