Just six minutes were on the clock when Otis Khan gave the Glovers the lead, with the winger on hand to tap in from close range after the Robins ‘keeper failed to gather Tom Eaves’ low cross.
The hosts’ lead was doubled after 16 minutes when captain Darren Ward converted Khan’s corner with a pinpoint header, leaving Gary Johnson’s side stunned.
With four minutes of the first half remaining Aaron Downes got a goal back for the visitors from a corner of their own, before Matty Dolan made it 3-1 minutes later with a fine diving header.
Town almost added to their lead in the second half through Eaves, but just before the hour mark Cheltenham made it 3-2 through Billy Waters after Danny Wright’s penalty was initially saved by Artur Krysiak, with the attacker alive after the ball was recycled.
Not to be defeated, Eaves scored a stunning solo goal in the dying embers of the game to round of an entertaining afternoon of football at Huish Park and secure another three points for Town.
Darren Way made one change to the side that picked up all three points at Leyton Orient last weekend, with Bournemouth loanee Ben Whitfield slotting into the midfield three in place of the suspended Kevin Dawson.
In an open start to proceedings at Huish Park the Robins almost took the lead with just a minute on the clock when Downes’ header back across goal was met by Harry Pell on the volley, but his effort flew just wide of the target.
After that early warning, Darren Way’s side took the lead with their first attack of the game after six minutes when Eaves’ powerful run and cross down the right wing could only be parried by Russell Griffiths, with Khan on hand to tap in from close range and give the hosts a dream start.
In a bid to get straight back into the game Harry Pell had an effort from 20 yards saved comfortably by Artur Krysiak, before the Glovers doubled their lead just past the 15-minute mark.
Eaves had a dipping shot from the edge of the box tipped over the bar and from the resulting corner, an expertly executed set-piece saw Khan turn provider when his cross was emphatically headed past Griffiths by captain Ward to give Town a 2-0 lead.
The onslaught continued and only a smart save from the Cheltenham ‘keeper denied Khan a second from the angle, before a combination of Daniel Parslow and Griffiths somehow kept out Hedges’ low cross which cause chaos in the six-yard box.
With the Robins unable to get into the game, Gary Johnson made two changes on the half hour mark introducing Jack Munns and Bill Waters for Easah Suliman and Jonny Smith, switching to a 4-4-2 formation.
The change brought some initial joy for the visitors as Aaron Downes headed home a Munns corner after 41 minutes to reduce the deficit, but Yeovil restored their two goal lead in first half stoppage time.
Khan, who the visitors couldn’t fathom out in the opening 45 minutes, skipped past two Cheltenham defenders before having a curling effort from inside the box saved by Griffiths, but the Robins keeper only found Dolan whose brilliant stooping header found the top corner from 12 yards to send Darren Way in happy at the break.
Town’s intensity continued after the break and Eaves came close to making it 4-1 after 48 minutes, but his glancing header from Khan’s whipped cross fell inches wide of the target.
Cheltenham were handed a lifeline just before the hour mark however, when Eaves was adjudged to have pushed a Robins player in the penalty box with the referee immediately pointing to the spot.
Danny Wright saw his spot-kick excellently saved by Krysiak, but with the ball still in play substitute Waters was on hand to tap in from close range to make it 3-2.
After conceding under unfortunate circumstances Yeovil looked to add a fourth goal and came close through Hedges, whose looping effort from just inside the box just cleared Griffiths’ crossbar.
Way made a double substitution himself after 67 minutes, introducing Bevis Mugabi and Alex Lawless for Darren Ward and Ben Whitfield respectively, meaning Alex Lacey took hold of the captain’s armband.
As the game entered the final five minutes Lawless almost made a telling contribution after coming on, but Griffiths produced a stunning point-blank save to tip over the Welshman’s header from a Hedges corner.
But the Glovers didn’t have to wait long to score a fourth, as Eaves rounded off an impressive delay with a stunning solo goal.
The striker breezed past Downes before rounding Griffiths and finding the net with the help of the post to round off a pleasing afternoon for Darren Way, as Yeovil claimed their second successive league win, sending former manager Johnson away empty handed in the process.
Yeovil Town: Krysiak; Shephard, Lacey, Ward (Mugabi 67’), Smith; Whitfield (Lawless 67’), Butcher, Dolan; Khan, Eaves, Hedges.
Bookings: Dolan 73’, Butcher 78’, Shephard 90.
Subs not used: Maddison, Ezewele, Copp, Sowunmi, Campbell.
Cheltenham Town: Griffiths; Suliman, Downes, Parslow, O’Shaughnessy; Smith (Munns 31’), Pell, Dickie, Suliman (Waters 31’); Dayton (Hall 81’), Wright.
Bookings: Wright 90’, Pell 90’.
Subs not used: Kitscha, Barthram, Morgan-Smith, Thomas.