The 20-year-old defender twice headed home unmarked in the opening half an hour before Ryan Flynn sealed the three points early in the second half.
Alex substitute Max Clayton grabbed a late consolation goal as his side slipped into the Sky Bet League One relegation zone, below Clough's team on goal difference.
Crewe captain Abdul Osman forced a save out of George Long with a powerful header early on before Maguire edged the Blades in front in the 18th minute when Stephen McGinn's free-kick from the left was allowed to bounce in the Alex area.
Striker Lyle Taylor was then denied by visiting goalkeeper Steve Phillips before Maguire nodded in his second from a McGinn corner after 29 minutes.
Crewe winger Byron Moore wasted a golden opportunity to reduce the deficit seven minutes after the break when he volleyed over while unmarked, moments before Flynn cut inside full-back Kelvin Mellor at the other end to score with a right-foot shot from the edge of the box.
Clayton raced clear in the 78th minute to slot in a reply for Crewe but United finished worthy winners.
- Sports & Recreation
- Ryan Flynn