In a game lacking clear-cut chances the green and whites possessed the only shot on target from the opening 45 minutes despite enjoying plenty of territory.
After the restart, opportunities remained at a premium before Yoann Arquin squandered the best chance of the match with 20 minutes to go.
In the final 10 minutes Tom James went close from a free-kick, but it wasn’t to be as both sides had to settle for a share of the spoils.
In action for the first time in 10 days, Darren Way made three changes from the side that last lined up in Sky Bet League Two.
Jordan Green, who scored in the 2-2 draw with Exeter City, dropped out with an injury to allow Rhys Browne a starting spot on the wing.
Forced into a second change, Sessi D’Almeida completed a one-match suspension for accruing five yellow cards to see Yoann Arquin come into the eleven, whilst in a final swap Gary Warren returned to captain the side in place of Shaun Donnellan in defence.
On the bench, goalkeeper Stuart Nelson returned for the first time this season after recovering from a calf injury along with Alefe Santos who missed more than a month with a thigh problem.
Bathed in late October sunshine the Glovers began in an equally bright manner, enjoying plenty of territory and possession.
Alex Fisher, looking for a second goal in as many league games, saw a looping header tipped over the bar by Scott Davies before Warren headed into the arms of the visiting stopper from a corner.
Earning plenty of set-plays, the deadlock was almost broken on 21 minutes by a stunning free-kick.
Fresh from netting at Colchester United at the start of the month James stepped up to shoot from 35 yards out and was almost rewarded, only for his swirling strike to whistle just wide of the post.
With Nathan Baxter a virtual spectator in the home goal Way’s side remained in control of possession as the clock ticked towards half-time but they couldn’t call Davies into action once again before the break.
Unable to get into Yeovil’s final third in the opening 45 minutes, Micky Mellon’s side registered a shot on goal just three minutes into the second half.
Jonny Smith’s cross looked for James Norwood at the front post but the striker couldn’t direct his flicked effort on target as it flew harmlessly wide.
Responding at the other end, Olufela Olomola fired a curling strike over the bar from the edge of the box before Browne had a goal-bound shot well blocked to keep Davies’ cleansheet intact as the hour-mark approached.
As the game continued to lack clear chances Darren Way made his first move, introducing Omari Patrick for Fisher to allow Yoann Arquin to move further forward.
The switch almost paid off immediately when Carl Dickinson’s free-kick delivery perfectly picked out Arquin six yards from goal, but the attacker couldn’t apply the finishing touch needed to make it 1-0.
Now into the final 10 minutes and looking like a game that would need something special or a mistake to bring an opening goal, James almost embarrassed the visiting keeper.
His swerving free-kick from 25 yards confused Davies between the sticks, who unconvincingly scooped the strike over the bar.
Proving to be the final meaningful attempt on goal it finished with a point apiece in Somerset, with Town now turning attention to the visit of Crewe Alexandra in midweek.
Yeovil Town: Baxter, James, Mugabi, Warren, Dickinson; Arquin, Pattison, Gray, Browne; Fisher (Patrick 67′), Olomola.
Bookings: James 84′, Dickinson 87′
Subs not used: Nelson, Mahmutovic, Donnellan, Santos, Rogers, Henry.
Tranmere Rovers: Davies; Caprice, McNulty, Sutton, Monthe; Smith (Cole 66′), McCullough (Harris 90′), Banks, Gilmour (Mullin 61′); Jennings, Norwood.
Bookings: Norwood 38′, Sutton 59′, Banks 82′
Subs not used: George, Mottley-Henry, Ellis.