It took until two minutes into the second half for Spartans to break the deadlock through Sean Reid, who quickly doubled that just a couple of minutes later. Paul Robinson made it game over with a third on 58 minutes, with Wilson Kneeshaw adding a fourth 20 minutes from time to leave Spartans seven points clear of the Quakers ahead of their Tuesday night trip to Frickley.
Hyde, meanwhile, are just a couple of points above the drop zone with four games to go to avoid back-to-back defeats.
Stourbridge secured three welcome points at Amblecote against the team immediately below Hyde, Stamford AFC, to move into the play-off places at the expense of Workington AFC.
Chris Lait opened the scoring on 36 minutes, curling in a superb shot from just outside the penalty area after good link-up play with Justin Richards. It took until three minutes from time for the game to be wrapped up and nerves calmed, Ashley Vincent tucking the ball home after Richards' initial shot had been blocked by Stamford keeper Paul Bastock.
Elsewhere, a first half double from Mike Williams proved enough for Ilkeston FC to end a run of nine league defeats in a row with a nervy and gritty win over third-bottom Whitby Town.
Williams opened the scoring from the penalty spot after 26 minutes and he doubled that seven minutes before the interval. Michael Roberts reduced the deficit with the night's second spot-kick on 66 minutes but the Robins held firm to keep the Seasiders three points behind Hyde.
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