The visitors' skipper Neil Austin made a brilliant block to deny Jordan Chapell in the opening minute when Derby loanee Callum Ball crossed from the left and he threw himself at the ball to charge away Chapell's close-range drive.
Ball's strike partner Karl Hawley then headed just wide from a Kevin Nicholson cross and then sent a right-footed drive flying past goalkeeper Scott Flinders as Torquay pressed for an opener.
The trend continued at the start of the second half with Ball denied by defender Christian Burgess after the striker pounced on an opportunity as Flinders spilled the ball.
Ball must have wondered what he had to do to score as another effort, in the 55th minute, was cleared off the line by Burgess.
Hartlepool's best chance fell to Bradley Walker in stoppage time but after prodding the ball past home keeper Martin Rice, he fired wide.