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Ross Lafayette's 85th-minute winner earned Welling their first victory of the season in The Skrill Premier on Saturday.
Lafayette's low shot proved the difference between Welling and former Football League side Grimsby in a game of few chances at either end.
The visitors may have felt that defeat was harsh on their efforts but Welling belied their part-time status in the final 20 minutes and finished the stronger side.
Neither keeper was seriously tested in a subdued first half. Both teams packed the midfield and cancelled each other out. Welling's Blaine Hudson missed their best chance, heading over from an Alex Dyer corner, while Grimsby went even closer on the stroke of half-time but Clayton McDonald headed a Patrick McLaghlin corner against the bar.
The game came to life just after half-time when a needless push by Lenell John-Lewis saw Welling defender Fraser Franks collide with a pitchside photographer. Most players converged on the incident and after much discussion referee Craig Hicks produced three yellow cards.
Welling lost skipper Lee Clarke to a head injury just before the hour mark, John-Lewis also coming off as the pair clashed heads in the penalty area. Welling introduced Harry Beautyman from the bench for his debut, 24 hours after he made the switch to Park View Road from Skrill South Sutton.
Dyer was the heartbeat of Welling's second half display and he got stronger as the game went on. Neat feet to buy himself time on the ball and an eye for the pass as well, Dyer nearly opened the scoring on 82 minutes but his left-foot curler went wide of the far post.
The winner came quickly after, however, when substitute Loick Pires and Dyer combined to set up Lafayette whose low left-foot drive found the far corner. Dyer was taken out as he played the ball on the edge of the area but referee Hicks played an advantage rather than give Welling the free-kick.
Substitute Dayle Southwell had a late effort beaten away by keeper Lee Butcher but Grimsby's attacking threat seemed to go with the exit of lone forward John-Lewis earlier in the half.