Phil Ifil gave the Lions a shocking start as he allowed Billy Jones' pass to roll under his foot to Steve Jones, who scored.
Barry Hayles's fifth goal of the season from the spot gave Millwall hope but it proved to be a false dawn.
Jermaine Wright gifted Gary Roberts the ball to make it 2-1 before Steve Jones shot home to wrap up the points.
Crewe boss Dario Gradi:
"That's the first away league victory since Boxing Day and it's not a relief, it's a pleasure to get three points.
"It has been a good week for us to get seven out of nine points.
"Steve Jones took his goals well but we were poor in the first half and I said so at half-time."
Millwall: Jones, Ifil, Lawrence (Cogan 66), Paul Robinson, Craig, Elliott, Dunne, Wright, Livermore, Dyer, Hayles.
Subs Not Used: Hutchison, Simpson, Masterson, Braniff.
Booked: Craig, Paul Robinson.
Goals: Hayles 38 pen.
Crewe: Williams, Moss, Walker, Foster, Tonkin, Billy Jones, Lunt, Gary Roberts, Vaughan (Moses 90), Steve Jones, Higdon.
Subs Not Used: Rivers, Johnson, Rodgers, Tomlinson.
Booked: Higdon.
Goals: Steve Jones 15, Gary Roberts 63, Steve Jones 70.
Att: 8,120
Ref: K Stroud (Dorset).