Blackpool had to survive a late Tranmere fightback to cling on after a first-half hat-trick by John Murphy.
The Seasiders went ahead after 19 minutes with their first real chance of the game when a powerful Kirk Hilton free-kick, which looked to be heading for goal, was turned past John Achterberg by the head of Murphy.
New Tranmere boss Brian Little saw his side go two goals behind thanks to a quick Blackpool break which saw Mike Sheron play in Martin Bullock, whose cross was bundled in by Murphy at the far post.
Little would have been furious at the third goal which came about through some sloppy defensive play by Graham Allen, who gave the ball to Murphy inside the area and saw the big striker slot the ball past Achterberg.
Rovers hit back after 78 minutes through a Shane Nicholson free-kick and another substitute Iain Hume gave the visitors hope with a second two minutes later, but there was to be no dream start for Little as Blackpool hung on.