Other than the holidaying Mark Newton, boss Dave Holmes selected from strength, with nine players signed in the off-season and keeper Jody Barford a last-minute arrival from Bridlington Town after first-choice stopper Dane Whittleston suffered a cut eye in the side's final warm-up in midweek.
But despite dominating the first half, Welfare finished second best, prompting manager Holmes to organise a midweek friendly in an effort to address some of his problems before the FA Cup tie with Teesiders Billingham Synthonia at Leeds Road on Sunday.
Renowned cup fighters, Billingham were only elminated from the FA Vase on penalties at the semi-final stage last season and Welfare will have to be much improved if they are to progress.
The visitors' created several goal-scoring chances in the early stages and it was no surprise when they took the lead with a sweetly-struck drive from Richard Britten, who was teed up by Michael Amos.
Four minutes later Paul Arkle shot wide when he should have done better and Ashley Beck curled a 25-yarder just around a post. It was 24 minutes before the home side offered any kind of threat when Barford saved comfortably from Matthew Styles.
On the half-hour Arkle shot wide from 25 yards but in the last five minutes of the half the home team enjoyed some pressure when first Styles shot just wide and then Joe Storer headed just over from a corner.
The half ended with Rob Poulter saving well from Beck following a corner. Welfare were good value for their half-time lead but could feel disappointed that it was only one goal.
On 55 minutes Richard Marchant was wide with an optimistic effort from 35 yards and within 60 seconds the game was turned on its head.
The visitors' defence was non-existent as Scott Ellis went clear and he rounded a hesitant Barford to level it up.
The goal galvanised Staveley, witih Styles twice going close and Ellis forcing a decent save from Barford.
Britten was cautioned for a tackle from behind on 72 minutes and the home team took the lead from the subsequent free-kick. Ellis' shot was blocked by Barford but Styles followed up to hammer the ball home.
Ryan Damms and Styles both went close to extending the lead in a reversal of fortunes and Glasshoughton showed little fight now, although Nigel Croad was unlucky to see a well-struck effort deflected high over the bar when it looked to be on target.
Holmes replaced Beck with Jack Kirk and Amos with Glen Shelley in a desperate effort to rescue something from the game but the pendulum had swung in the favour of Staveley, who made the game safe in the final minute when Ellis went clear and rounded Barford to hit number three.
Welfare: Barford, Targett, Mattison, Croad, Dobson, Britten, Arkle, Marchant, Beck (Kirk), Amos (Coppinger), Jackson (Shelley).