Crewe boss Dario Gradi told crewealex.net: "Luke has waited for his chance, I wanted to introduce him to the Crewe public and he was lively."
It will be a relief for Rodgers to finally make his first appearance in the Championship as he bids to get his season going.
Elsewhere, other high profile Town departures Ryan Lowe and Sam Aiston have impressed at their new clubs Chester and Tranmere. Lowe has five goals and Aiston has figured prominently in Tranmere's first string.