A hat-trick from Lincoln's in-form striker Jamie Forrester stretched Barnet's winless run to eight games and keeps them in the relegation zone.
The first real chance of the game fell to the home side when Magno Vieira was denied by Lincoln's Alan Marriott from close range midway through the first half.
The miss proved costly as the visitors went one up just minutes later when a poor clearance from Barnet skipper Ian Hendon fell to Lincoln's Scott Kerr.
Kerr picked out an excellent run from Lee Frecklington who burst through the defence and squared the ball to Forrester who side-footed the ball into an empty net.
Forrester then doubled the lead on 33 minutes when he was brought down inside the box by Barnet keeper Ross Flitney.
The 31-year-old Forrester, who missed from the spot against MK Dons earlier in the season, picked himself up and tucked the resulting penalty away.
The visitors were now in complete control of the game and it was soon three when the Barnet defence failed to clear Kerr's free-kick and ball fell kindly to Lee Beevers who stabbed it into the roof of the net from a couple of yards out.
Things got worse for the home side after the break when Frecklington was felled in the box and the replacement referee Simon Cook - who came on for Clive Penton at half-time after he became unwell - pointed to the spot.
The dangerous Forrester sealed his hat-trick from a confident strike from 12 yards.
Frecklington was unlucky not to get on the scoresheet himself midway through the second half when his shot from just inside the box was headed off the line by Barnet's Anthony Charles.
The visitors finally made it five when second-half substitute Leon Mettam scored his first goal for the club in injury time.