Danny North's first-half brace sealed the result for the Mariners making in their first win for eight League Two outings.
In the match programme, Fairclough had praised Grimsby's midweek FA Cup win over League One table-toppers Carlisle, and suspected that Alan Buckley's team would be on a high after Tuesday's victory.
Fairclough was also aware that every time Grimsby had previously visited Barnet they had grabbed all three points. The last time they met in Grimsby, Barnet were swept away 5-0.
Barnet's League form has also been stuttering of late with the Bees only gaining two points from their last five League outings.
New loan signing Rob Atkinson looked composed at the centre of defence all game for Grimsby, an addition which looks likely to improve the Mariner's defensive record of only one clean sheet all season.
With only ten minutes on the clock Barnet failed to clear a corner, which resulted in North finished from close-range. His second, on the stroke of half-time, was even more calamitous from a Barnet perspective.
Ismail Yakubu had been motioning to the bench that his groin had gone, but it was his poor pass that allowed North to pick Kenny Gillet's pocket on the halfway line.
He then shook off Gillet and outpaced Sagi Burton, before neatly finishing passed the helpless Lee Harrison.
North's substitute in the second half, Andy Taylor, iced the cake with a cool finish with a minute remaining.