The League One match really came to life ahead of half-time with three goals in the space of eight minutes.
Iain Hume fired Tranmere in front in the 38th minute with an excellent left-foot shot when set up by Ian Goodison as the visitors hesitated in defence.
Blackpool levelled it out in the 44th minute. Home keeper John Achterberg did well to keep out a long range effort by Rory Prendergast, but could not hold the ball which fell to Scott Vernon who netted from close range.
The Seasiders were caught out in first half injury time when Tranmere swept from defence for Chris Greenacre to mark his home debut with a super shot into the top right-hand corner from Hume's through ball.
There might have been goals earlier on in the contest as Blackpool keeper Lee Jones produced a super save to deny Gareth Roberts in the 33rd minute, and then, two minutes later, Achterberg did well to keep out a header by hardworking midfielder Keith Southern.
Tranmere were right out of luck in the 63rd minute. Greenacre fired against a post and from the rebound Roberts struck the underside of the bar.
Blackpool levelled for a second time in the 70th minute, with John Murphy powering home a header from a corner by Keigan Parker.
Hume almost snatched it for Tranmere late on, but was inches wide from a cross by Sam Aiston.
Blackpool deserved their point, and each side is yet to win after two outings.