Goals from Jamille Matt and Sam Jones in each half meant that Mark McGhee's first home game in charge of Barnet ended in a loss to Grimsby.
The former Aberdeen manager freshened up his team by handing league debuts to teenagers Benjy Aghadiuno and Dwight Pascal with the latter receiving a straight red card for a strong sliding challenge in the 54th minute.
The Bees started brightly but it was the visitors who took the lead in the sixth minute when Matt headed in from Luke Summerfield's corner.
Shortly after the goal, Jamie Stephens made a fingertip save to stop Sam Jones' header.
In the 54th minute, Pascal's debut was cut short as he received his marching orders by referee Gavin Ward for a tackle on Siriki Dembele.
The Mariners capitalised on the numerical advantage in the 75th minute after Dembele found space out wide to lay the ball off to Jones who doubled the visitors' lead.
The result leaves Barnet in the relegation zone, one point from safety.