Neither side created much in an opening 45 minutes that was devoid of any excitement at both ends of the pitch.
The Blues looked dangerous after the interval, but were unable to breach an increasingly over-worked Glovers defence.
Paul Cook made three changes from the side that suffered a first league defeat against Exeter on Tuesday night.
Skipper Michael Doyle returned to the midfield in place of Danny Hollands, while Conor Chaplin and Jayden Stockley dropped to the bench to make way for Gary Roberts and Matt Tubbs.
Yeovil named a couple of familiar faces in their starting line-up, with Ryan Bird and Wes Fogden both featuring.
The first half was a low-key affair played out in bright autumn sunshine, with neither keeper having much to do.
There were plenty of balls into the box and blocked half-chances, but little to excite another packed Fratton crowd.
Pompey were producing plenty of patient passing football, although they were unable to unlock the Glovers defence.
And it was the visitors who came closest to breaking the deadlock when Matt Clarke was dispossessed on 22 minutes, but his defensive partner Christian Burgess quickly slid in to deny Harry Cornick.
Then, from the resulting corner, Bird diverted the ball goalwards, only to be denied by Aaron McCarey.
The Blues’ best chance also came from a corner, with Doyle launching a fierce volley that flew narrowly past the post.
Pompey did start to look more threatening towards the end of the half, but a couple of dangerous Kyle Bennett crosses could not be converted.
Yeovil Town 0
Cook made a switch at the break, with Jayden Stockley on for Gareth Evans as the hosts switched to a 4-4-2 system.
But they were still lacking that incisive final ball to breach Yeovil’s back-line and test keeper Artur Krysiak.
The Fratton faithful were doing their best to inject some life into proceedings, with constant chants of ‘Blue Army’ ringing around the ground.
It almost had the desired effect just past the hour mark when Ben Davies delivered a fine cross that somehow managed to evade the waiting Stockley.
The right-back tried to find the same player again moments later, but this time the striker could not beat Krysiak with a header.
Pompey were suddenly looking threatening and Roberts was next to have a chance when he met Bennett’s cut-back and powered inches over the bar.
A second substitution followed on 70 minutes, with Danny Hollands coming on for Adam Barton in the middle of the park.
It was Bennett who tried to bring the game to life soon after, though, when he surged inside from the left and fired in a shot that was blocked.
The ball then sat up nicely for Tubbs, but a Yeovil player managed to get in the way and Hollands’ follow-up suffered the same fate.
Pompey had their opponents camped back in their own half, with a succession of corners causing plenty of problems.
One of them fell to Doyle 30 yards out and his fierce drive had to be smartly parried clear by Krysiak.
The Blues continued to pour forward in the closing stages, as their under-pressure visitors struggled keep hold of the ball.
But Yeovil held firm until the final whistle to frustrate Pompey and ensure a share of the spoils.
Pompey (4-2-3-1): McCarey; Davies, Burgess, Clarke, Stevens; Barton (Hollands 70), Doyle (c); Evans (Stockley 46), Roberts, Bennett; Tubbs (Chaplin 89)
Subs not used: Bass, Webster, Tollitt, Naismith
Yeovil (4-1-4-1): Krysiak; Roberts, Arthurworrey, Sokolik (Howells 66), Smith; Fogden; Cornick (Laird 79), Sheehan (Jeffers 90+2), Dolan, Dickson (c); Bird
Subs not used: Weale, Lacey, Allen, Bassett
Referee: Darren Deadman
Attendance: 17,309 (612 away fans)