The visitors played their part in an entertaining affair on a greasy surface, but were blown away by a three-goal City blast inside 12 second-half minutes.
Les Davies gave City the perfect start, beating keeper Dave Roberts to head home after just two minutes in front of an all-ticket 2,593 crowd.
And when a long ball from Peter Hoy found Sion Edwards, the midfielder recovered from a slip to beat floundering defender Chris Davies and slip the second past Dave Roberts.
But, after a hesitant start, the Seasiders started to find their feet and player-manager Neil Gibson danced through the City defender to reduce the arrears midway through the half.
Home keeper Lee Idzi made a superb save to tip a Dan Evans shot over the bar before Steve Rogers spurned a gilt-edged chance to make his 300th Welsh Premier appearance with a goal.
with the game finely poised going into the final half hour, Dave Morley eased home nerves with a superbly-struck 25-yarder which flew into the top corner. A Chris Jones cross was swept into the net by Craig Garside before Ross Stephens again reduced the deficit from the penalty spot after Jamie Brewerton had handled in the box.
Morley was on hand to claim his second after a Chris Jones cross was farmed across goal by Davies, but Mike Parker claimed the last goal to be scored at the famous old ground as the second-half scoring spree came to an end.