Goals from Luke Murphy, Bradden Inman and Mathias Pogba were enough for all three points despite Paul Huntington's late reply for the hosts, just 24 hours after Davis put pen to paper on a new 18-month rolling contract with the Railwaymen.
Murphy put Crewe in front against the run of play, finishing low under the body of Thorsten Stuckmann when Byron Moore's pass found him unmarked in the area.
Five minutes after half-time Crewe had doubled their lead through Inman, the on-loan Newcastle youngster slotting in off the post for his first senior goal.
And just three minutes later Pogba's 10th goal of the season put the game beyond any doubt, the striker meeting Moore's cross and finishing at the second attempt after Stuckmann saved his first effort.
Huntington headed home a minute from time but it was not enough to prevent Preston extending their winless run at home in the league to six games.