The Glovers continued their climb up the League One table as goals from Paul Warne, Aaron Brown and Shaun MacDonald secured a fourth successive victory.
Town took a two-goal lead in the first half at London Road, with Warne and Brown both netting from crosses into the Peterborough box.
The home side pulled a goal back after the break through Aaron McLean, but a horrendous error from home keeper Joe Lewis then handed Shaun MacDonald a crucial third goal for the Glovers.
After a slow start, the game exploded into life midway through the first half, with Peterborough first to threaten.
On 25 minutes Craig Mackail-Smith burst past Terry Skiverton and bore down on the Glovers' goal.
But Josh Wagenaar raced out to confront the Posh striker and made an impressive save as he dived at Mackail-Smith's feet.
The Peterborough front man also headed a good chance over the crossbar as the home side demonstrated their quality going forward.
But Yeovil shocked Darren Ferguson's side by taking a 30th minute lead as they capitalised on Posh's weakness defending crosses.
Andy Welsh sent the ball across from the right wing, Aaron Brown flicked and Paul Warne dived in to force the ball over the line from close range.
And just three minutes later the Glovers doubled their advantage in similar fashion from another Welsh cross.
The winger fired a free-kick into the box and Brown again reacted ahead of the Posh defence to flick the ball into the corner of the net with the outside of his foot.
Peterborough tried to hit back before the break and McLean came close to pulling a goal back when he latched on to a George Boyd pass before firing just wide.
And midfielder Jon Worthington saved his side as he cleared a McLean header off the line just seconds before the interval.
Yeovil had to weather an onslaught from the home side at the start of the second period, with Boyd and Chris Whelpdale both coming close.
And Posh's pressure told on 56 minutes when Whelpdale and Boyd combined to set up McLean, who fired a low shot into the corner of the net.
Boyd then twice came close to an equaliser with long-range efforts before Wagenaar saved his side with a brilliant save from the home left winger.
But on 70 minutes the Glovers sealed an impressive victory with their third goal, a strike which owed everything to a horrendous error from home keeper Joe Lewis.
Town midfielder Shaun MacDonald fired in a speculative shot which Lewis had covered but somehow allowed to squirm from his grasp and roll into the net.
Wagenaar made one more impressive save before the final whistle to keep out a McLean shot which deflected off Lee Peltier, but Yeovil comfortably held on to record their fourth successive victory.
