The Tigers quickly showed their teeth with goals by Steve Pickford, Gareth Seddon and Dale Johnson giving them a 3-0 half-time lead.
And though Leigh goalkeeper Jon Lamb repeatedly stood between Hyde and an even bigger slaughter, he was powerless to prevent Matty Tipton adding two more after the break to seal a triumph which takes Steve Waywell's side up to second place.
Kieran Lugsden pulled one back for the third-from-bottom home side.
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