After a bright start from both sides, it was Lincoln who opened the scoring through Jordan Burrow, who was found at the back post to head home from close range.
Barnet responded positively, but they were dealt a further blow on 22 minutes when Hamza Bencherif was well positioned to send a header past the goalkeeper at the back post.
The home side, who had scored seven times without conceding in their first two fixtures, ended the half on top, but after Lee Cook had seen a first-time strike kept out, Lincoln were able to retain their advantage until the break.
After the restart, it took just 11 minutes for Barnet to get back into the match when Charlie MacDonald provided a cross for Keanu Marsh-Brown, who kept his composure to fire a composed finish into the corner.
Barnet soon pushed for a second, but they were nearly dealt a sucker punch when Nat Brown hit the crossbar with a header before Burrow lashed wide inside the penalty area.
Ben Tomlinson was proving to be a huge threat for Lincoln in the final third, but he failed to make the game safe for his side with two missed opportunities inside three minutes.
The closing stages of a thrilling encounter were dominated by the home side but, despite Akinde and MacDonald being provided with half chances inside the penalty area, they were unable to find a leveller as Lincoln hung on for the win.