Goals from Tom Hamer, Erik Ring and Reeco Hackett secured victory for the Imps despite a valiant display from Travis Binnion's side.
Shea Lacey and James Scanlon both went close for United across the 90 minutes, but our best chance fell the way of Jack Fletcher.
The midfielder was denied by City defender Lewis Montsma with his strike almost certain to find the net, if not for a fine goalmouth interception.
FIRST HALF
It took 16 minutes of toing and froing before Binnion's side had a meaningful attempt on goal, with Scanlon stinging the palms of Zach Jeacock with a near-post effort.