Barnet raced into a 3-0 half-time lead thanks to two goals in 15 minutes from Kabba and a fine Mark Hughes strike.
But two Lincoln goals in the first five minutes after the restart from Luke Howell and Ashley Grimes put the result in doubt, only for Izale McLeod to make the game safe late on.
Kabba took his season's tally to seven after heading home a Mark Marshall corner on six minutes and then scoring a spot-kick 11 minutes later when Jordan Parkes upended Ali Fuseini.
A first win in nine looked wrapped up with Marshall 's superb curled effort on 38 minutes, but the Imps had other ideas as Howell and Grimes scored in quick succession after the restart.
However, McLeod restored the hosts' comfortable advantage with 22 minutes remaining to lift Barnet out of the relegation zone by a point.