This was largely due to some excellent goalkeeping from Donovan Ricketts and the central defensive pairing of David Wetherall and Mark Bower.
Yeovil looked like taking the lead in the 25th minute when Leon Best, on loan from Southampton, embarked on a powerful run which took him through the defence but he was thwarted by an excellent save from Ricketts.
Two minutes later Chris Cohen tried a 20-yard blockbuster which flew just over the bar.
Little was seen of City's attack in the early stages and it was 33 minutes before they got in a shot. Dean Windass brought home keeper Steve Mildenhall to his knees from just outside the box.
Just before the break, Best was set up with another good chance. Lee Morris did the spadework on the left and his cross was accurate but Best failed to make clean contact with the header.
If Yeovil had had more of the play in the first half, their domination was even more evident in the second.
Best fired straight at the keeper and Arron Davies was inches over from 25 yards.
In the 62nd minute Martin Brittain provided an excellent cross from the right which Morris just failed to reach and Best was again just over eight minutes later.
Each side had a chance in the closing stages. From a Yeovil corner a powerful header by Cohen was tipped over by Ricketts, and on 87 minutes Windass was just wide with a 20-yard effort at the other end.
Windass, who scored an 87th minute goal to win the corresponding fixture for City last year, was again a constant thorn in Yeovil's side. When he wasn't winning free-kicks he was conceding them and his performance belied his 37 years.
City have now taken seven points out of 12 and, with two home games to come, look capable of pushing on towards the play-off places.