Town made a bright start to proceedings and had an Alex Fisher goal ruled out for offside before Alefe Santos called Scott Flinders into early action.
Having been on the back foot, the visitors then scored twice in 10 minutes as first Luke Varney and then Conor Thomas – thanks to a dubious penalty decision – put the Robins in a commanding first-half position.
However, Cheltenham were pegged back after just 47 minutes when Tom James’ free-kick nestled in the back of the net to reinstate the Glovers’ position in the match.
A relentless attack after the restart Fisher struck the post amongst a host of chances as an equaliser threatened, but it was Michael Duff’s side who put the game to bed on 77 minutes when Jordon Forster restored the two-goal cushion.
Adding to a difficult afternoon Kevin Dawson emerged from the bench for Cheltenham to score against his former club and complete the scoring.
Opting for continuity, Darren Way named an unchanged side for the second time in three matches.
The hero last time out at Huish Park, Yoann Arquin kept his place on the left wing as Rhys Browne started amongst the substitutes once again.
Facing a Cheltenham side full of familiar faces, Scott Flinders and Ben Tozer started against their former employers whilst previous fan-favourites Dawson and Craig Alcock started on the bench.
The latter had to wait just 10 minutes to enter the fold with his introduction for the injured Johnny Mullins the only point of note in a quiet start to proceedings.
It wasn’t until the 11th minute that either side eventually threatened, with the Glovers suddenly bursting to life.
Neat work from Francois Zoko on the left-hand side of the box saw him pick out an unmarked Jordan Green in the middle, but his shot from the penalty spot was scuffed wide.
Sparking a two-minute spell crammed with chances, the hosts thought they’d taken the lead when Fisher headed home Arquin’s inch-perfect cross only for the linesman to rule it out for offside.
Staying on the front foot, Zoko burst into the box and rounded visiting goalkeeper Flinders only to go down and be booked for simulation by referee Trevor Kettle moments later, with a third chance quick to follow.
Intricate play on the edge of the box saw Alefe Santos played in by Zoko to go one-on-one with the Robins’ number one, but the stopper was quick off of his line to produce a smart stop.
All happening inside first 20 minutes it suggested a positive half for the green and whites, but the Gloucestershire outfit were quick to respond and took the lead with their first meaningful shot on goal.
Jacob Maddox’s through ball found the run of Varney perfectly, with the experienced striker keeping his composure to curl a strike past an advanced Stuart Nelson.
Having denied Town a penalty at one end Kettle had a decision to make at the other just after the half-hour mark when Chris Hussey seemed to go down easily under challenge from Sessi D’Almeida.
Much to the surprise of virtually all inside Huish Park the man in black pointed to the spot, giving Thomas the chance to double the lead which he managed from 12 yards.
Comfortable with their 2-0 advantage Michael Duff’s side were able to hold the Glovers at arm’s length, heading into half-time in a commanding position.
Making the most of the 15-minute break the Glovers re-emerged looking like a different outfit and were immediately on the score sheet.
D’Almeida’s bursting run won a free-kick on the edge of the box wide on the left, giving James the opportunity to fire a free-kick around the wall and into the back of the net courtesy of a deflection off of the unfortunate Thomas.
Galvanising the home supporters the green and whites continued to flood forward and the chances continued to flow.
Latching onto a ball over the top Green let fire with a venomous strike which forced Flinders to parry, as Fisher went even closer minutes later when his shot from inside the box came back off the post before being scrambled away.
When on another day he’d now be chasing a hat-trick, Town’s top scorer went close to equalising again before the hour-mark when Fisher’s curling effort from 20 yards whistled just over the bar.
Adding fresh legs in a bid to keep the green and whites on the front foot Browne replaced Zoko with a little over 20 minutes remaining, as Green moved forward into a more advanced position.
Losing their tempo displayed in the first 20 minutes of the second half the Robins came back into the match and after winning a corner ensured the three points would be leaving Huish Park with them.
Hussey’s corner was headed back where it came from by Tyrone Barnett to give Forster the easy job of stabbing home from a yard out.
With all the promise of an equaliser now evaporated the result got worse for the hosts in the closing stages, as Alex Addai’s cross was steered into the net by Dawson who respectfully marched back to the halfway line without celebrating.
James almost added a second of the afternoon when his low drive came back off the post but there was to be further consolation as 2019 began with defeat.
Yeovil Town: Nelson; James, Warren, Gafaiti, Dickinson; Green, Santos, D’Almeida, Arquin (Arnold 87′); Zoko (Browne 67′), Fisher (Olomola 80′).
Bookings: Zoko 15′, Dickinson 76′, Gafaiti 79′
Subs not used: Baxter, Mugabi, Donnellan, Gray.
Cheltenham Town: Flinders; Forster, Tozer, Mullins (Alcock 10′); Thomas, Atangana, Clements, Hussey; Maddox (Barnett 60′), Addai, Varney (Dawson 84′).
Bookings: Forster 46′
Subs not used: Lovett, Jones, Bower, Mooney.