Albion carried out Micky Adams' instructions to perfection by proving they can win without Bobby Zamora.
Adams motivated his players by warning they would be regarded as a one-man team if they lost.
The Seagulls responded with their first away victory in the League for two months, courtesy of Zamora's stand-in.
Gary Hart has found himself almost exclusively out on the right flank since Adams changed to a 4-3-3 system at the start of September.
He scored with a lucky deflection off former team-mate Jamie Campbell when partnering Zamora in the pre-Christmas success against Exeter.
There was nothing flukey this time about the strike which completed a hat-trick of 1-0 triumphs for Albion at Underhill.
Paul Watson played a corner back to Richard Carpenter and Hart swivelled onto his cross-shot to plant a volley past Lee Harrison from eight yards.
Hart saved Watson from feeling like a Christmas turkey.
Two minutes earlier Albion's normally reliable penalty taker had been horribly high from the spot after Rob Sawyers fouled Paul Brooker.
Hart made sure that didn't matter and also vindicated Adams' team selection.
He decided not to give the fit-again Darren Freeman his first start since the end of August.
Adams opted instead for Hart through the middle, an immediate recall for Nathan Jones on the left and Brooker on the right.
All three played their part. Indeed, Harrison's diving stop from a Jones shot set up by Brooker produced the corner for Hart's matchwinner.
Charlie Oatway also had a fine match to give Albion the initiative in the midfield battleground, but one player stood out.
Danny Cullip was colossal. He snuffed out the threat of Tony Cottee and co and almost scored a goal of outrageous quality for a centre half.
Cullip dribbled around three opponents, including Harrison, early in the second half before Sawyers foiled him with a goal-line block.
Cullip had Andy Crosby alongside him in the absence of Matthew Wicks through the hamstring injury he sustained against Exeter.
That ruined a showdown for Wicks with dad Steve, Barnet's new coach, who may now be wishing he had stayed as an agent.
This was his first home match following a nightmare start at Hartlepool 72 hours earlier.
Cottee recalled himself after that 6-1 debacle and also Scott McGleish, so loathed by Albion fans for his past contributions for Leyton Orient.
They were kept quiet and Michel Kuipers was hardly troubled to keep another clean sheet.
Cottee failed to connect properly early on with a right-wing cross from the subdued Darren Currie.
McGleish was also restricted to an angled half-volley narrowly over the bar just before the interval.
He should have done much better though with a free header from another cross by Currie shortly after the break, which he glanced well wide.
That sort of scare was rare for the commanding Seagulls and they could have doubled their advantage either side of a flurry of late substitutions.
Oatway's effort from long range bounced just wide, then Freeman's angled shot in stoppage time was blocked by Harrison.
Barnet finished with ten men, midfielder Warren Goodhind receiving his marching orders moments later for a second bookable offence.
He had already been cautioned in the first half for a foul on Hart when he brought down Carpenter.
Adams said: "We were very solid. We won our individual battles and restricted Barnet to very few chances.
"We weren't the tallest of teams and I was worried about their set pieces, but I thought Jones, Hart and Brooker's pace would cause them problems.
"The first time Paul Brooker was really positive and went for the jugular we got a penalty.
"The only problem we have is if we get too many more injuries.
"We've got two at the moment (Wicks and Lee Steele). Any more than that and we are struggling."
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