Two goals in the first half-hour by experienced striker Mark Stallard earned the victory for the Imps, although Hereford's Rob Purdie reduced the arrears with a late penalty.
Hereford were pressed back by the visitors in the early stages and it came as no surprise when the Red Imps, after creating openings through Stallard and Jamie Forrester, took the lead on 11 minutes.
Goalkeeper Scott Tynan, who had only just been introduced to his new team-mates, could only watch in horror as a Stallard shot deflected off former Rushden & Diamonds team-mate Phil Gullliver and looped into the net.
That was the start of a good phase for Lincoln who continued to attack and completely shackle Hereford's forwards.
Tim Sills did force a couple of flying saves from goalkeeper Alan Marriott, but it was the visitors who posed the greater threat and they increased their lead on 29 minutes.
Livewire forward Forrester raced down the left and produced a perfect cross for Stallard to leap above Gulliver and power a header past Tynan.
And the Imps might have added a third three seven minutes later when Jeff Hughes' header from a Ryan Amoo cross came back off a post.
Hereford made a brighter start to the second period and should have reduced arrears on 53 minutes when Andy Williams blazed a good chance over from ten yards.
But Lincoln could never be discounted as an attacking force and a Forrester header from Amoo's cross clipped the outside of a post on its way behind.
But Hereford gave themselves fresh hope when Purdie scored from the penalty spot after Sills had been fouled.
And the Bulls thought they had levelled when Alan Connell forced the ball home only to see the goal disallowed for offside.
Then, eight minutes from time, a superb shot on the turn by Stuart Fleetwood was thwarted by an even better save from Marriott.