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Welling had Blaine Hudson red-carded as Aldershot claimed a flattering victory in the Skrill Premier on Saturday.
While the hosts enjoyed plenty of possession, they lacked a cutting edge until three goals in the final quarter of the game - once Welling were down to 10 men - handed them victory.
Jake Goodman headed wide for Aldershot from an early corner and keeper Lee Butcher had to beat away Jordan Roberts' near-post drive but that was the only save he was called upon to make in the opening half.
Hudson collected his first caution on 32 minutes for a shirt-pull, although he will later point to Aldershot players making the same offence and receiving no bookings from referee Wayne Barratt.
It needed an excellent block by De'Reece Vanderhyde to deny Aiden O'Brien a clear sight of goal while Welling's best opening saw Ross Lafayette head wide from a Jamie Day free-kick.
Welling started the second half brightly and Hudson headed Day's corner wide before the latter saw his 20-yard free-kick pushed away by keeper Glen Morris.
The resulting corner gave Welling the opening goal on 50 minutes as Day's deep delivery was headed goalwards by Lafayette and a missed clearance on the post handed the Wings striker his 10th goal of the season.
Aldershot failed to register an effort at goal after the break until they were given a lifeline on 66 minutes. Hudson was left overloaded at the far post and his push on Joe Oastler was punished with a second caution and spot-kick. Brett Williams sent Butcher the wrong way from the spot.
The 10 men held their own until 11 minutes from time when O'Brien was given space to run at the Welling defence, although his 20-yard shot needed a deflection to find its way past the dive of the wrong-footed Butcher.
Aldershot's Roberts was only booked for shoving Kurtis Guthrie after the latter's late challenge on Morris with seven minutes left before the hosts wrapped the game up on 86 minutes when O'Brien headed in a near-post free-kick.
Substitute Luis Cumbers nearly pulled one back for the Wings with virtually the final kick of the game but his shot was blocked by the onrushing Morris.