The Alex striker had already hit the woodwork from 25 yards before he fired them ahead from David Vaughan's pass.
Mark Rivers crashed home the second from eight yards from another Vaughan cross before Daniel Harding's 30-yard effort for Albion hit the woodwork.
Vaughan again crossed for Ashton to tuck in his third, meaning Paul Reid's 25-yard strike was a mere consolation.
Brighton boss Mark McGhee
"It's total frustration not having a striker to bring in but there's nothing I can do.
"Considering the shackles that we're under, in not having the funds to buy a
player, this is probably the most frustrated that I've felt.
"To stay up we need 50 or 51 points and if we manage that come
the last day of the season it will be fine. I don't care what anyone says our performance was not totally disappointing.
"We were forced to play a different way because of Virgo's absence and Crewe
exploited it. But had we scored the first goal the result would have been
Crewe boss Dario Gradi
"We didn't pass the ball particularly well in the first half and we
have plenty to work on.
"When you target away points, Brighton is a place you want to come to and get
something from, so it's pleasing we took advantage."
Brighton: Kuipers, Hinshelwood, Cullip, Butters, Mayo, Currie, Reid, Nicolas, Harding, Knight, Piercy (Hammond 57). Subs Not Used: Oatway, Carpenter, El-Abd, Roberts.
Booked: Knight, Hammond.
Goals: Reid 85.
Crewe: Ince, Billy Jones, Lunt, Foster, Sorvel, Cochrane, Ashton, Vaughan, Tonkin, Rivers, Otsemobor. Subs Not Used: Walker, Steve Jones, Varney, Tomlinson,
Goals: Ashton 40, Rivers 50, Ashton 59.
Ref: B Curson (Leicestershire).