With thick fog limiting visibility, Town came closest to scoring when Otis Khan’s effort cannoned back off the woodwork late in the second half.
Artur Krysiak had to be alert to deny Kai Naismith twice in the opening 45 minutes, but Darren Way’s side had the League Two high flyers on the back foot for large spells.
After drawing 0-0 with Exeter City on Boxing Day, Way made one change to the side that started last time out.
Ryan Hedges, ruled out with an ankle injury picked up four days ago, had his space wide on the Glovers right filled by Tahvon Campbell, whilst Ollie Bassett came into the squad having returned from a loan spell at Dorchester Town.
In what would’ve made a good setting for a horror film, Huish Park slowly became engulfed by fog in the opening minutes of the match, meaning picking out a green and white shirt on the far side of the pitch became an increasingly difficult task.
The conditions led to a disjointed start to proceedings, but it was Pompey who found their feet first amongst the haze in the opening stages.
Looking menacing wide on the left, Kai Naismith produced the first meaningful attempt on goal with 14 minutes on the clock, forcing Artur Krysiak to tip his effort from the angle over the bar.
The Portsmouth wideman continued to be at the centre of everything good for the visitors, with his corner being headed just wide by defender Matt Clarke, before another Naismith delivery caused chaos in the middle, this time with Michael Smith glancing a header just wide.
Despite Portsmouth’s early endeavours, Town enjoyed an even share of possession in the opening 45 minutes and, masked by thick fog towards the Radio Cabs Away End, Ben Whitfield flashed a shot wide before Otis Khan saw a free-kick from range land in the arms of David Forde.
Ever dangerous, Naismith went even closer on 37 minutes when he volleyed Smith’s knockdown goalwards from close range, but Krysiak used every fibre of his frame to claw away the effort which was destined for the bottom corner.
Looking to end the half on a high, Campbell wriggled free in the Pompey box to engineer a yard of space, but his shot on the turn was deflected into the arms of Forde.
The hosts began the brighter of the two sides after the break and a neat pass from Campbell almost played in Whitfield but for the covering of Christian Burgess, before Town earned a succession of corners.
Unable to capitalise on the set-pieces Portsmouth produced their first chance of the half when Noel Hunt fired into the arms of Krysiak from the edge of the box, whilst Kevin Dawson did the same at the other end.
As the game entered the final 20 minutes both sides began committing numbers forward in search of that elusive opening goal, with Way introducing Francois Zoko for Campbell in a re-shuffle up front.
With Eaves now playing wide on the left the goal scorer almost turned provider when his cross looked destined for Zoko at the back post, only for the ball to ricochet off two Pompey defenders and into Forde’s arms.
Pressing, the hosts went even closer on 84 minutes when Khan raced through on goal, but under pressure from Stevens the 21-year-old was unlucky to see his powerful shot come off the angle of the crossbar and post and evade Eaves on the follow up.
That was as close as either side came to breaking the deadlock, as the Glovers had to settle for a share of the spoils despite having Paul Cook’s side on the ropes.
Yeovil Town: Krysiak; Shephard (Mugabi 21’), Lacey, Smith, Dickson; Dawson, Lawless, Whitfield (Butcher 81’); Khan, Eaves, Campbell (Zoko 71’).
Bookings: Dickson 90’.
Subs not used: Maddison, Ezewele, Bassett, Sowunmi.
Portsmouth: Forde; Evans, Burgess, Clarke, Stevens; Baker (Chaplin 81’), Rose, Doyle (Linganzi 90’), Naismith; Hunt (Bennett 67’), Smith.
Subs not used: O’Brien, Whatmough, Lalkovic, Buxton, Bennett.