Dominant from the kick-off, the Cumbrians never allowed Crewe to threaten in a first half peppered with long distance shots.
But seven minutes after the break, Garner finished neatly to break the deadlock and fire Carlisle into second place in the league table.
The Cumbrians had forced Crewe on to the back foot from as early as the fifth minute when Jeff Smith struck a low drive which flicked off the outside of Ben Williams' post.
Danny Graham then drove a shot straight into Williams' arms and within seconds, Crewe's Nicky Maynard bundled his way past two defenders but could only poke his shot over the bar.
Graham immediately had another shot easily saved before Chris Lumsdon fired narrowly wide from 25 yards.
Carlisle were now in total command and Simon Hackney should have scored when well placed with just Williams to beat.
Garner's through ball found the winger ten yards out but he somehow managed to screw his shot wide when a goal seemed certain.
On 50 minutes the home side went even closer when Graham craned his neck to head David Raven's cross against Williams' crossbar.
But within two minutes, Carlisle finally got the breakthrough when Zigor Aranalde's cross was dummied by Graham allowing Garner to steal a yard on his marker and side-foot past the stranded Williams.
The Crewe keeper then pulled off an excellent save to deny Hackney when he flung himself to tip the deflected shot wide having initially gone the other way.
After falling a goal behind, Crewe tried to rally and, although Byron Moore found the target, Carlisle keeper Keiren Westwood saved easily and the point for the visitors never looked likely.