There were no goals, but plenty of thrills from two positive teams.
Rovers had more chances as they extended their unbeaten run to 18 games, but Hartlepool hit the post early on and had what looked a penalty turned down in the closing minutes.
Defender Michael Nelson hit the woodwork, sending his header against the post after a corner in 13 minutes.
Ten minutes later, Pools went close again as Matt Robson's shot from wide on the left forced its way through a crowd and was just wide of the far post.
But then Iain Hume started to shine. Pools keeper Jim Provett saved his stooping header on 31 minutes, and seven minutes later he was convinced he had scored with a curling 25-yard free-kick, but Provett pulled off a fine save as he dived to his left to gather the ball in mid-air.
After the break it was Hume again who looked like breaking the deadlock, but home striker Eifion Williams cleared his header off the line and then Provett pulled off an even better saved as he switched to stop the striker's angled shot after he burst into the area.
But it was never one-sided and Hartlepool were always in it. They took over in the closing stages and several long-range efforts went astray before they had a penalty turned down when Ryan Taylor appeared to handle in the area.
But neither side deserved to lose and a goalless draw between the new boys and a side determined to play a part in this season's promotion race was a fair one.
Tranmere boss Ray Matthias agreed with that and said: "We were on top in the first half, and perhaps should have scored. But we missed our chances and then in the second we defended well when we had to." Hartlepool manager Neale Cooper said: "Tranmere are a very good Second Division side and this is a good result against them.
"Four points from our first two league games is a good return."