The point leaves Pools six short of safety in League One's relegation zone, while it keeps the Glovers in fifth spot in the play-off race.
Neither side could find a breakthrough in an attritional affair.
It was 35 minutes before there was a direct threat on goal, when the visitors' leading goalscorer Paddy Madden thundered an angled drive off the underside of the crossbar, which bounced off the goalline to safety.
Ritchie Humphreys then curled a shot wide for Pools right on half-time.
Pools goalkeeper Scott Flinders made a low save to deny Ed Upson a goal in the 50th minute before the midfielder took possession from a throw-in to shoot across Flinders, who saved.
From a Glovers' counter-attack, James Hayter sent a weak header at Flinders from close range after taking a pass from Madden.
Pools' best chance came in the 84th minute when substitute Antony Sweeney broke clear, but he poked his shot too close to Yeovil goalkeeper Marek Stech, who saved without much trouble.