They were always in control against a Crewe side who had put together a decent sequence of results, staying unbeaten for three games against tough opposition in Swansea, Leyton Orient and Leeds. John Ward's promotion-chasers proved to be a bridge too far for the Alex, who remain in the bottom four after this defeat.
In a dreadful first half which was hampered by the swirling wind, there were few clear-cut chances. Danny Graham hit a rising drive into Crewe keeper Ben Williams' hands and Joe Garner flicked a powerful header over the crossbar. Influential midfielder Marc Bridge-Wilkinson pulled the strings as Carlisle tightened their grip over the proceedings.
Peter Murphy tested Williams again with a strong shot from outside the box, but the clearest chance of the half fell to home strike Byron Moore in stoppage time. But Carlisle keeper Keiren Westwood made a terrific double save to keep out two efforts from Moore in quick succession at the far post.
That was the closest Crewe came to breaking the deadlock and in the second half Carlisle began to turn the screw. The home side had a lucky escape on just over the hour-mark when Williams made a complete hash of clearing George Abbey's back pass. He sliced the ball and it trickled fortunately for him the wrong side of the post.
But there was no reprieve when Dobie finished clinically three minutes later. The striker replaced injured leading scorer Garner at the break and he gave Williams no chance with a drilled finish to Taylor's pinpoint cross. Crewe went in search of an equaliser and Gary Roberts saw his thumping header tipped over by Westwood, but it was Ward's side who held on deservedly for a decisive win.