Gillingham skipper Mike Flynn hammered home the only goal of the game to deny Crewe a deserved point at Priestfield.
The former Wigan midfielder smashed home a 25-yard rocket in the 71st minute, giving Ben Williams no chance.
But that was harsh on the Alex who paid the ultimate penalty for not taking their chances.
Ryan Lowe had a corner cleared off the line before Michael Higdon blazed over from close range and Sean Miller was denied in the dying minutes.
Gillingham: Larrieu, Southall, Sancho, Johnson, Jackman, Bentley, Flynn, Crofts, Spiller (Chorley 85), Mulligan, McDonald (Ndumbu-Nsungu 85).
Subs Not Used: Cox, Pugh, Collin.
Goals: Flynn 71.
Crewe: Williams, Woodards, Baudet, O'Donnell, Moss, Lowe, Cox, Jones, Roberts (Pope 86), Jack (Miller 73), Higdon.
Subs Not Used: Tomlinson, Bignot, Carrington.
Ref: R Lee (Essex).