The Pars lost their opening game to current leaders Ross County but then beat Inverness Caledonian Thistle (1-0), Ayr United (1-0) and Partick Thistle (3-0).
Dunfermline continued their good form into March by defeating Queen of the South 1-0 to move into the promotion play-off places.
Crawford, a former Scotland midfielder, took over as manager at East End Park in January following the departure of Allan Johnston.