Hyde slipped to their seventh defeat in nine Blue Square Bet Premier matches at the hands of Tamworth.
The Lambs twice went close through Tom Marshall in the first half, but finally went ahead after the break when Sam Oji bundled home.
Danny Lloyd's effort then deflected in off Tommy Wright to seal victory for the hosts.
Chris Sedgwick compounded the away side's misery when he was sent off for two bookable offences.
The Tigers are now just two points above the drop zone having played at least a game more than their relegation rivals.