Alassana Jatta netted his 13th goal of the season in the 19th minute to leave County second in the table, 11 points behind leaders Walsall.
Paul Glatzel, Harry Smith and Kabongo Tshimanga scored from the 87th minute onwards as Tranmere finished with nine men.
Lee Bell believes Crewe’s players will learn from a tough spell which has seen their League Two promotion credentials given a thorough examination.