The 30-year-old kept out spot-kicks from Gary Roberts and Kenny Lunt in either half as they maintained their promotion push.
Lee Barnard put the visitors ahead when the home defence crumbled as he sneaked through to score.
Southend doubled their lead when Alan McCormack fed James Walker and Ben Williams could not prevent him scoring.
Crewe were thrown a lifeline after 33 when Nicky Maynard was fouled in the box by Peter Clarke, but Roberts saw his penalty brilliantly saved.
Flahavan was the hero again 17 minutes from time, saving Lunt’s effort after Simon Francis hacked down Maynard and although Maynard headed home Lunt’s cross a minute later, Barnard completed the scoring 10 minutes from the end.