Full-time score from The Hive
There was to be no giant-killing act for Martin Allen's Bees, and once striker John Akinde had put the ball into his own net after 18 minutes, The Lions didn't look back.
Aiden O'Brien doubled their tally nine minutes before the break before second-half efforts from Steve Morison (74mins) and a Fred Onyedinma penalty with nine minutes remaining, secured an easy passage into the Second Round draw.
There was a new full-back pairing too as Joe Martin came in at left-back and Sid Nelson on the right whilst Jimmy Abdou's return in central midfield for Shaun Williams completed the quintet of changes.
Neither team really created much going forward in a somewhat scrappy opening quarter of an hour in which Lions defender Martin picked up a booking for a clumsy challenge on Akinde.
The game sprung into life in the 18th-minute when Millwall broke the deadlock, albeit with a huge slice of luck thanks to the boot of Bees' striker Akinde, who rather spectacularly sliced Martin's free-kick from the right wing into his own net from 10 yards out.
Akinde looked to make amends and it took a great tackle from Byron Webster to put the ball behind for a corner as the burly front man broke behind the visiting back line and prepared to shoot on the half-hour mark, although there were a few steely looks from the Millwall players towards the linesman who had not flagged for offside.
The Lions doubled their tally four minutes later when Morison's flick to Onyedinma was blocked, but the ball fell invitingly for the onrushing O'Brien, who confidently buried a shot into the back of the net for his second goal in as many games.
Barnet nearly reduced the arrears with a Jean-Louis Akpa Akpro header that flew wide of the target, but The Lions had the measure of their opponents and were rarely troubled in the opening 45 minutes.
In fact Millwall could have added a third goal seconds before the break when a thumping header from skipper Tony Craig flashed a yard past the post with the last action of the half.
The home side desperately needed to get an early foothold back in the game and it took a smart save from keeper Jordan Archer to keep out Ryan Watson's shot as it arrowed towards the bottom left corner.
The Lions responded positively with Onyedinma's header from an O'Brien delivery blocked moments before the striker's audacious long range effort dropped onto the roof of the net.
Sub David Worrall, a 67th-minute replacement for O'Brien took just four minutes to register a goal assist as his perfectly flighted corner from the right was met by Morison whose firm header squeezed between keeper Josh Vickers and the upright to put Millwall 3-0 ahead.
Some delightful footwork from Morison so nearly conjured up a fourth goal for Harris' men barely 60 seconds later, but his final shot was straight int the hands of Vickers.
Credit to Barnet, however, who kept plugging away with Watson twice sending efforts fizzing wide of the target before a combination of keeper Archer and midfielder Ben Thompson somehow kept the ball out with a double goal-line clearance.
At the other end Millwall continued to look dangerous and when some supreme control by Onyedinma eventually drew a foul from two bewildered Barnet defenders, referee Dean Whitestone pointed straight to the spot. There was only one player going to take the penalty - Onyedinma - and one place he was going to put his shot...in the back of the net for goal number four!
There was still time for Worrall, Thompson and Onyedinma again, to try their luck but further goals would perhaps have been a tad harsh on a Barnet side who gave their all, but simply could not match the clinical finishing of their free-scoring opponents.
Bookings: Togwell (36mins), Gash (84mins)
Millwall: Archer, Martin (Ferguson, 82mins), Craig, Thompson, Onyedinma, Wylde, Nelson, Webster, Morison, O'Brien (Worrall, 67mins), Morison (Philpot, 79mins), Abdou. Subs not used: Williams, Gregory, Romeo, King.
Booking: Martin (12mins)
Scorers: Akinde (23mins, og), O'Brien (34mins), Morison (74mins), Onyedinma (81mins, pen)
Ref: D. Whitestone
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