This 'East v. West' clash was played on a very soft pitch which didn't lend itself to a flowing game.
Both sides had their chances in the first half but what proved to be the winner came when Daniel Kelly struck three minutes from the break.
The second half saw a number of substitutions as the condition of the pitch started to take its toll on fitness.
As the game progressed Carrick where unlucky not to double their advantage as Dergview 'keeper Jack Bogg saved a point blank shot from Ben Roy.
Gary Haveron's side now join Lisburn Distillery, HW Welders and Bangor in Tuesday night's semi-final draw.
Daniel Kelly celebrates after scoring the match winner
Goalmouth scramble
Dergview's Colin Robinson receives the man of the match trophy from Robbie Walker of the IFA Intermediate Cup Committee