Ash Taylor wasted a big chance for Tranmere when he headed over in the 15th minute from a corner. Joss Labadie then shot just wide from 30 yards.
Nathan Jones blasted over from the corner of the box for Yeovil and Paul Wotton hit the defensive wall with a free-kick.
At the start of the second half, Anthony Edgar saw a good effort deflected for a corner and the same player brought a good save from Rovers goalkeeper Owain Fon Williams after 70 minutes.
Substitute Lucas Akins headed wide for the hosts 10 minutes from time when he might have done better.
Town sub Kieran Agard raced clear in the 87th minute but David Raven got back to make a last-ditch tackle.