Jake Gallagher's first goal of the season maintained Welling's impressive home form on Saturday.
The Wings have lost just once at home all season, the points picked up at Park View Road providing the foundation for their current position of eighth in the Skrill Premier.
And they grinded out the victory against a Lincoln side, who have now scored just once in their last four league matches.
Lincoln's Ben Tomlinson had the first chance, racing clear on nine minutes only to be denied by a fine block from Welling keeper Lee Butcher.
Veteran keeper David Preece responded at the other end with an equally impressive stop to keep out Joe Healy's 30-yard left-foot shot from a short free-kick.
Then, from the resulting corner, Preece somehow kept out Blaine Hudson's far-post header.
Butcher produced a one-handed save to turn behind Marlon Jackson's effort, later touching over a long-range shot from the same player and then Sean Newton sent a free-kick wide of the upright.
The inventive Healy produced the one moment of magic in the game eight minutes after the break. Gallagher showed more desire than the visitors to win a loose ball on the edge of the box and Healy's clever flick sent the Wings midfielder clear, his low left-foot finish proving too good for Preece.
Tomlinson then headed wide a golden opportunity to equalise before Kurtis Guthrie failed to find the necessary power at the other end as chances continued for both sides.
The closest Lincoln came to an equaliser was on 67 minutes when Welling defender Fraser Franks headed a left-wing cross straight at his own keeper when attempting to clear.
Franks then had a header at the right end well saved by Preece before Jackson's free-kick, which clipped the outside of the post with 12 minutes left, was Lincoln's best chance as the Wings held on with some ease in the latter stages.