Jon-Paul McGovern gave the visitors the lead in stunning fashion with a tremendous 40-yard free-kick midway through the first half of Tuesday night's League One clash at the Broadfield Stadium.
Reds goalkeeper Paul Jones flapped at the ball weakly as it went in off the underside of the crossbar.
Cumbrians defender Danny Livesey should have hit the target shortly before when heading wide from a McGovern corner.
The hosts finished the first half strongly and winger Nicky Adams had a fierce free-kick parried away by Mark Gillespie, before he again denied Adams by turning his volley round the post.
Richie Barker's side equalised 11 minutes after the break through Sadler, who rifled home from 18 yards into the roof of the net after being set up by Mike Jones.
Jamie Proctor could have clinched it for Crawley when he wastefully headed an Adams cross over the crossbar before Carlisle substitute David Symington's 25-yard free-kick was well saved by goalkeeper Jones.