Crewe 1-0 Preston
Brad Inman's goal was enough to keep Crewe's faint play-off hopes alive as Preston went four games without a win.
Home keeper Alan Martin had to make saves from Graham Cummins and Joe Garner, while Declan Rudd kept out an Inman effort at the other end.
But the Australian notched his eighth of the season when firing in Kelvin Mellor's cutback.
Lee Holmes struck the Crewe woodwork but the Alex clung on to go within 10 points of the League One play-offs.