The visitors enjoyed the better of proceedings but couldn’t find a way past an imperious Artur Krysiak to claim all three points in Sky Bet League Two.
A point sees the Glovers move three unbeaten at home, having picked up all seven of their points in front of the Town faithful.
Darren Way opted to give the eleven that lost at Crawley a week previous a chance to make amends, sticking with the same starting line-up for a third league match in a row.
Having signed on deadline day, loanee Matt Worthington started amongst the substitutes for his involvement as a Glover in the only change to the matchday squad.
On a blustery afternoon in Somerset it was the visitors who started with the wind in their sails, threatening to break the deadlock in the early exchanges.
A superb last-ditch Ryan Dickson challenge stopped Mohamed Eisa firing a shot off from inside the box, before his strike partner Danny Wright missed a gilt-edged opportunity with 12 minutes on the clock.
Eisa’s low drive came back off the post falling perfectly to Wright, who somehow trickled an effort wide of the target with the goal begging.
Creating chances inside the opening 20 minutes, Carl Winchester’s low cross couldn’t be turned goalwards by Eisa, as the Robins proved wasteful in front of goal to the relief of the Glovers.
Far from clinical, Cheltenham manager Gary Johnson ruthlessly replaced Wright with Jaanai Gordon after 23 minutes, in a bid to find an end product.
Despite remaining unscathed from the early onslaught, the Glovers struggled to recreate the attacking form from their opening two home matches to the frustration of the home faithful.
Rounding off a one-sided opening 45 minutes, Jordan Cranston had a long-range strike palmed away by Krysiak, leaving Town to require a livelier second half.
As they did at Crawley last weekend the Glovers made one switch at the break, as Jordan Green replaced Olufela Olomola who seemed to be struggling with a knock.
However, before the alteration had chance to affect the pattern of play the Robins were back on the front foot after the restart.
The lively Gordon forced Krysiak into a diving save from a venomous drive, before Sam Surridge replaced Rhys Browne in a bid to get Town ticking in the final third.
It remained a defensive effort up to the hour mark however, as Krysiak produced a stunning double save to keep the score at 0-0.
Town’s Polish stopper was quick off his line to smother Eisa’s effort, before recovering to tip Gordon’s curling strike over the bar just seconds later.
The smart double save seemed to invigorate Way’s side, who engineered their first chance of the match after 67 minutes.
Otis Khan’s jinking run worked space in the box to allow a cross, which could only be glanced wide by an advanced Bevis Mugabi.
Having struggled to exert pressure on Cheltenham the Glovers grew into the game in the final 20 minutes, led by the influence of Green.
At the other end Jerell Sellars had a shot from range pushed away by the impassable Krysiak, before Khan fired into the arms of Scott Flinders from all of 25 yards.
With virtually the last act of the match substitute Hinds fired an effort into the side-netting forcing both sides to share the spoils, as Yeovil move three games unbeaten at home.
Yeovil Town: Krysiak, Mugabi, Nelson, N. Smith, Dickson, Browne (Surridge 52’), C. Smith Gray 75’), Bailey, Khan, Zoko, Olomola (Green 45’).
Bookings: Nelson 36’
Subs not used: Maddison, Davies, James, Worthington.
Cheltenham Town: Flinders, Winchester, Moore, Grimes, Cranston, Dawson, Storer, Pell, Morrell (Sellars 70’), Wright (Gordon 23’), Eisa (Hinds 61’).
Bookings: Cranston 78′, Hinds 89′
Subs not used: Flatt, Boyce, O’Shaughnessy, Bower.