Wolves suffered a first-round FA Cup exit following a 2-1 defeat to Oldham in their replay at Molineux
Crewe live updates
Harry Maguire's first-half brace helped give new Sheffield United manager Nigel Clough a dream start.
The 20-year-old defender twice headed home unmarked in the opening half-hour at Bramall Lane before Ryan Flynn sealed the three points.
Alex substitute Max Clayton grabbed a late consolation as his side slipped into the relegation zone, below the Blades on goal difference.
Hearing the Crewe coach is stuck in traffic on the M1. Not sure how far away they are #SUFC
Crewe Alexandra manager Steve Davis has said the club is in talks with Arsenal over bringing midfielder Chuks Aneke back on loan.
@crewealexfc Thank you for leaving your changing rooms so tidy. Credit to professional football. All the best for the season ahead.
Crewe have signed midfielder Anthony Grant on a free transfer from Stevenage
The 26-year-old has left Boro by mutual consent and agreed a two-year deal at Gresty Road.
Leeds United have completed the signing of Crewe Alexandra captain Luke Murphy, with the midfielder signing a three-year deal at Elland Road.