Looking dangerous from the start, Alex Fisher and Omar Sowunmi both went close inside the opening 90 seconds before the hosts enjoyed their own spell of pressure.
Coming out the other side unscathed, the Glovers dominated the remainder of the half and two goals from Alex Fisher on 34 and 36 minutes secured a healthy halfway lead.
Town’s number nine completed his hat-trick after the break before Yoann Arquin rounded off the scoring in a stunning display.
In Nottinghamshire for their third game in six days, Darren Way was forced into one change from the side that started against Aston Villa on Tuesday.
Reece Cole, who limped out after half-an-hour, dropped from the squad with Alex Pattison coming in to make his full debut.
Cole’s absence saw Jake Gray feature for the first time in six months after a lengthy injury lay-off to supply a positive alongside a host of casualties.
Stuart Nelson (calf), Shaun Donnellan (thigh), James Bailey (knee), Rhys Browne (hamstring), Francois Zoko (knee) and Cole (knee) joined the suspended Jordan Green on the sidelines.
Despite their mounting list of absentees the Glovers were quick out of the blocks with two chances inside the opening 90 seconds.
Intercepting midway inside the Magpies half, Diallang Jaiyesimi quickly fed strike partner Fisher who forced a smart save from Ross Fitzsimons with a first-time shot.
From the resulting corner, Carl Dicksinon’s delivery picked out Omar Sowunmi but the Town captain headed a yard over the bar in what was almost a perfect start.
After a rocky opening five minutes, Kevin Nolan’s side composed themselves and produced their own flurry of chances.
Nathan Thomas had the ball in the back of the net only to be correctly denied by an offside flag before Shaun Brisley headed a wife free-kick over the bar in a lively opening 10 minutes.
Continuing to be an end-to-end affair the Glovers squandered a glorious chance to take the lead when Wes McDonald’s low cross was somehow directed wide by Arquin six yards out.
Learning from their mistakes in midweek the visitors weren’t going to continue to squander chances and netted a quickfire double just past the half-hour mark.
Causing endless problems out wide, Arquin danced his way into a crossing position against his former employers before delivering it on a plate for Fisher to tap in.
With the home crowd still grumbling from the first goal Town added a second in similar fashion.
McDonald from the other side teased in another low cross which the 28-year-old was again perfectly placed to turn into the back of the net to give Way’s side a buffer at the break.
Exercising the old adage of attack being the best form of defence Town remained on the front foot after the restart and came within millimetres of making it 3-0 on 53 minutes.
Jaiyesimi isolated Brisley in the box and after finding space looked to have picked out the top corner only for a stunning Fitzsimons stop to tip the strike onto the bar.
With the hosts unable to gain momentum – to the disgust of the home supporters – it was Yeovil who continued to look the most likely in front of goal.
As the hour-mark came and went, Jaiyesimi continued to tease the Magpies defence and the Norwich loanee drew a smart diving stop from the home stopper after twisting and turning on the edge of the box.
More than holding their opponents at arm’s length the green and whites put the game beyond doubt on 71 minutes when Fisher rounded off a night to remember.
Beating the offside trap and latching on to Pattison’s superb ball, Town’s number nine fired in off the post from the angle to kill off any hopes of a home comeback.
On a night where lady luck seemed to be on the side of the Somerset outfit the Magpies then missed a chance to notch a consolation after Carl Dickinson was adjudged to have pushed Enzio Boldewijn in the box.
Awarded the penalty, Kane Hemmings stepped up but cannoned his spot-kick off the bar as Nathan Baxter’s goal remained unscathed.
Becoming a night to remember, Town confirmed their dominance in the closing stages by adding a fourth courtesy of former County player Arquin.
The winger rose highest to meet Dickinson’s inch-perfect ball to round off a stunning night in Nottinghamshire which saw the Glovers pick up all three points on the road.
Notts County: Fitzsimons; Hewitt, Duffy, Brisley, Jones; Boldewijn, Vaughan (Crawford 57′), Husin, Thomas (Kellett 57′); Dennis (Stead 68′) Hemmings.
Bookings: Brisley 45′, Crawford 83′
Subs not used: Culverwell, Bird, Alessandra, Hawkridge.
Yeovil Town: Baxter; James, Sowunmi, Warren, Dickinson; Arquin, D’Almeida, Pattison, McDonald (Gray 84′); Jaiyesimi (Henry 87′), Fisher.
Bookings: D’Almeida 30′, Baxter 81′
Subs not used: Phillips, Mugabi, Santos, Clarke, Rogers.