The Alex are now eight games without a win and are firmly rooted in the relegation zone.
There was a moment of controversy in the 26th minute when Crewe's Vadaine Oliver fired a shot into the net off the underside of the crossbar.
Referee Andy Haines had blown a second earlier after spotting Adam Dugdale lying prone inside the area. Oliver clearly felt the goal should have stood and turned with a look of surprise to find the game had been stopped for the injury.
But the corner was only cleared as far as Dave Symington 20 yards from goal and he blasted a shot through a crowd of players which seemed to glance off O'Hanlon's head as it flew into the net.
That goal came in the last minute of the first half, but Carlisle were not finished and in the second minute of injury time Miller headed on to Robson who cracked a left-foot shot past Etheridge from 18 yards to double the lead.
Carlisle were a crossbar's width away from a third early in the second half when James Berrett's 25-yard rocket cannoned off the woodwork with Etheridge beaten.
Matt Tootle served a reminder that the Alex were not out of it when he made space for a shot from 25 yards which had on-loan Manchester United goalkeeper Ben Amos at full-stretch to palm for a corner.
Oliver looked sure to score in the 75th minute when finding a huge gap in the home defence, but Amos produced a great save.
Davis reduced the arrears deep into added time with a downward header from six yards, but it came too late to save the visitors.
- Sports & Recreation
- Matty Robson