Argyle attacking midfielder Jason Banton scored a superb solo goal on 30 minutes, sweeping past a handful of defenders on a run into the visitors’ penalty area before sending a measured shot into the far corner of Scott Flinders’ goal from the left.
Pools midfielder Jack Barmby levelled in the 67th minute after latching on to Plymouth defender Durrell Berry’s bouncing back pass to lob keeper Jake Cole.
United substitute Jack Compton came close to winning the game with a shot that came back off the foot of the post with four minutes left.
Plymouth skipper Conor Hourihane also hit the frame of the goal with a 20-yard free-kick in stoppage time.
Argyle – who had lost five of their previous six league games – twice came close to taking the lead through target man Enoch Showunmi before Banton’s exquisite opener.
Showunmi flashed a spectacular scissor-kick shot over on 25 minutes not long after sending a dipping half volley over the angle from 20 yards.
In the first half United’s impressive playmaker Connor Oliver went close with an audacious 40-yard effort.