Crewe's first away win since April was wrapped up in the opening 12 minutes.
Finding space 18 yards out, Miller rifled in a low angled shot leaving Howarth to pick the ball out of the net - his first touch - in the third minute.
Nine minutes later Miller bagged his second from a quick fire-break after the luckless Howarth had made a good save.
Crewe's Colin Daniel outstripped the hosts' Michael Liddle and, although Howarth rushed out to block, Miller was on hand to plant the rebound into the empty net from the edge of the box.
From that moment the visitors stood back and allowed Carlisle to dominate possession, leaving Howarth, a late replacement for the sick Ben Williams, little more than a bystander.
But at the other end the Cumbrians struggled to find a way through past the impressive Stuart Tomlinson.
His good two saves denied Cleveland Taylor and David Raven before another quick break from Crewe saw Colin Daniel's goalbound shot blocked.
Further chances for the hosts arrived for the hosts when Jeff Smith blasted into the side-netting, and Gary Madine fizzed a header narrowly wide.
A stinging second-half volley from Marc Bridge-Wilkinson was tipped onto the post by Tomlinson, and that was as close as Carlisle came to scoring and getting back into the game.
When substitute Michael Bridges stung Tomlinson's palms with a smart first-time drive, and Madine had a good penalty appeal turned down, the hosts knew it wasn't to be their day.