Stephen Baxter's side held IF Bromma to a draw and with a little luck could have signed off their Europa League campaign with a famous win.
Despite trailing 4-0 from the first game, the Crues were determined to salvage some pride on the night and they made a solid start with Paul Heatley on the end of a Richard Clarke cross but his effort lacked any power to trouble the keeper.
Bromma went close to opening the scoring but were denied thanks to a fine double save by O'Neill in the home goal.
A few minutes later and the ball was in the net, but it was Crusaders who were celebrating after skipper Colin Coates powered a header home on 17 minutes.
It should have been 2-0 soon after but Cockcroft was denied by the woodwork and then Coates failed to hit the target when well placed.
Heatley then set up Chris Morrow but his effort was blocked as Stephen Baxter's side kept up the pressure.
However, despite all the good work the Crues were caught out at the back when Rexhepi nipped in to score from a tight angle on 28 minutes.
The second half continued to be very competitive but with no clear cut chances until Rexhepi fired over from a good position.
Crusaders had chances to win on the night with Heatley curling a shot wide and both Jordan Owens and sub Gary McCutcheon denied by the keeper.