The visitors twice equalised but goals from Luke Williams, Jordan Buckham (2) and Josh Dodd earned Welfare their second league win of the season.
Armthorpe now have six points to their name in Division One but have only played four games - fewer than anyone else.
Welfare grabbed the lead on six minutes when Leon Larcombe-Loftus sent over a cross which Jordan Buckham headed down and Williams showed a striker’s instinct to nip in and score as the Town defence hesitated.
The joy was short-lived as within a minute Skegness were back on level terms, Jordan Smith firing past Stevens following a swift attack.
Armthorpe pushed for a second and Dodd forced the visitors’ goalkeeper into a fine save from just outside the box.
The home side regained the lead on 24 minutes when Buckham beat the goalkeeper to a high ball and hooked the ball into an empty net from the edge of the area.
Skegness came back once more and scored a second equaliser just after the half hour mark when Smith again found the net with an angled drive which beat Adam Stevens with the aid of a deflection.
Welfare were back in front for a third time on 38 minutes.
Dodd saw his volley well saved by the Town goalkeeper but Liam Radford retrieved the ball and sent over a cross for Dodd to get the final touch almost on the line.
Dodd was unlucky not to score his second at the start of the second half with a diving header that thumped against the post.
Skegness remained a threat and Armthorpe were indebted to Stevens for keeping the lead intact.
However, Welfare gained some breathing space when they went 4-2 up on on 74 minutes. Williams cut in from the left to unselfishly square the ball for Buckham to convert from 12 yards.