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Welling boss Jamie Day branded his side "clueless" after they became the first team to lose to Hyde in Skrill Premier this season on Tuesday.
The Wings were outplayed and outclassed by a Hyde team who had lost 23 and drawn four of their previous 27 league games.
Without 11-goal leading scorer Ross Lafayette in attack through injury, Welling lacked any quality in forward areas. Day, Jake Gallagher, Jack Obersteller and Loick Pires were all ruled out through injury while skipper Lee Clarke, who didn't take part in the pre-match warm-up, was clearly lacking full fitness when he came on as a second-half substitute.
But Day refused to blame the defeat on a thread-bare squad, grateful instead to keeper Lee Butcher for a series of fine saves that prevented an even bigger margin of defeat.
Kurtis Guthrie went through for Welling on 10 minutes but his low shot was saved by keeper Lawrence Vigouroux and that set the tone for the hosts.
Connor Hughes' deflected shot went just wide, Butcher had to beat away Scott Spencer's fierce drive and then gratefully saved the rebound.
Josh Brizell's long-range free-kick was turned away for a corner before Blaine Hudson needed to make sure he timed his challenge right on the edge of the area to deny Spencer a clear run on goal.
Hyde's pressure nearly paid off on 39 minutes but Fraser Franks was back in time to clear off the line from Spencer after hesitation between Butcher and Hudson.
Welling forced a series of corners in the second half but most failed to clear the first man, and their biggest threat came from two mis-hit crosses that had to be tipped over the bar.
Hyde went ahead on 58 minutes with a goal from the game's stand-out performer, Louis Almond. Cutting inside from the left he unleashed an unstoppable 25-yard drive beyond Butcher.
Day turned to Clarke and Kiernan Hughes-Mason to provide his team some inspiration with 27 minutes left but a change of formation failed to bring any improvement in their ability to pick a team-mate out with a pass.
Vigouroux did well to save from Clarke and Doug Bergqvist but Hyde were well on their way to victory when Hughes hooked the ball home with 19 minutes remaining.
The visitors' luck appeared to have turned with four minutes left when a rare defensive mix-up saw Hughes-Mason hauled down in the box after a defensive header back went beyond Vigouroux but referee Daniel Cook amazingly waved away calls for a spot-kick.
There was, however, nothing lucky about Hyde's deserved victory and Day - who hopes to sign Bournemouth's Josh Wakefield on loan this week - admitted afterwards it was the worst Welling performance during his four years in charge at Park View Road.