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Blackpool opened the scoring in the sixth minute when Wes Hoolahan broke forward with the ball and fed Parker on the right wing.
The Scottish winger's cross was meant for fellow frontman Andy Morrell but Carlisle defender Peter Murphy got his head to it first only to see the ball bounce over keeper Keiren Westwood and into the back of the net.
The visitors - backed by an enthusiastic travelling support of almost 1,900 - enjoyed the lion's share of possession but created few chances and were punished for the lack of killer instinct just before the half-hour mark.
Parker began and ended the move, playing in a good through ball for Andy Morrell to chase and the former Coventry striker looked to have blown his chance by taking the ball too close to Westwood in goal. However, he looked up and picked out Parker's clever run with a neat cross which was tapped into the empty net.
Carlisle almost pulled one back through a header by veteran centre-half Kevin Gray and Blackpool keeper Rhys Evans had to be down sharply at his near post when Karl Hawley's snap-shot came close to beating him.
Carlisle continued to control much of the play without making an impact on the scoresheet until the 73rd minute when striker Derek Holmes nodded down for Hawley to fire home.
That seemed to wake Blackpool up and substitute Claus Jorgensen was inches from finding a crucial third, although there were occasional shaky moments at the back with Evans forced into a good save from a shot by former Blackpool loanee Chris Lumsdon.