Birchall, who opened the scoring midway through the first half, provided a goal threat throughout, while Albert Adomah and Anthony Thomas also got themselves on the scoresheet in a dominant display by the home side.
Further goals from Birchall and a first Bees goal by Max Porter gave the home side a deserved five-goal lead, before Ben Wright's late double finally gave Lincoln something to cheer about.
After Mark Stallard's delicate chip had threatened to give Lincoln the lead, Barnet stepped through the gears on a blustery day at Underhill.
But that was the closest the visitors were to come in a hugely one-sided affair as Barnet made the most of some shambolic Lincoln defending.
Despite the difficult conditions, Barnet produced some scintillating football in the first-half and Birchall should have put the hosts ahead when he met Nicky Nicolau's exquisite curling cross, only to divert the ball inches over the crossbar.
But the former Arsenal man made amends soon after, latching on to Nicolau's through ball before slotting the ball past Alan Marriot with ease.
That goal was no less than Barnet deserved and it came as no surprise when Adomah doubled their lead just 12 minutes later.
The exciting young winger showed great pace and poise to escape the attention of the Lincoln defence and, after working his way into the penalty area, Lee Ridley's reckless challenge sent the midfielder tumbling to the deck.
Mr Moss wasted little time in pointing to the spot and Adomah picked himself up to slam the penalty past Marriot with aplomb.
With Lincoln in disarray at the back, Barnet sensed a golden opportunity to kill the game off before the break and both Birchall and Thomas went close to adding a third.
But with just a minute of the first half remaining, the hosts did find the third goal their dominance deserved as Birchall's pin-point cross picked out Thomas in space and the striker's fizzing effort gave Marriot no chance.
Lincoln might have hoped for better in the second half, but their misery took a further blow less than 60 seconds after the restart as Birchall grabbed his second of the afternoon.
Once again it was Nicolau that provided the cross from the left and Birchall took advantage of some mediocre Lincoln defending to flick the ball beyond the reach of Marriot from close range.
With the snow falling incessantly across the field of play, both teams began to struggle in the treacherous conditions.
But despite the best efforts of Mother Nature, there was nothing that was going to stop Barnet in such irrepressible form.
Lincoln failed to clear their lines following a Barnet throw-in and Porter slammed a first-time effort past Marriot from 20-yards.
With the snow now making conditions near impossible, Barnet ploughed forward in search of increasing their lead further only for Thomas to slip at the vital moment when through on goal.
Lincoln rallied briefly and Wright volleyed home his 10th of the season after good work by Jamie Forrester with 14 minutes remaining.
Wright bundled home his second just three minutes later after some sloppy home defending afforded the striker the freedom of the penalty area to fire past Lee Harrison.
But there was to be no great escape for City as Barnet recorded a second consecutive home victory in style.