Meanwhile, despite recording four successive draws over the same period, bottom-of-the-table Grimsby are 10 points adrift of safety.
There was a time this season when Barrow appeared destined for an immediate return to the National League after an uninspiring opening six months in this division.
However, the caretaker appointment of Rob Kelly has acted as a much-needed catalyst, the Bluebirds having now recorded four successive wins with three clean sheets.
While Barrow twice let slip leads against Crawley Town at the weekend, Chris Taylor's last-gasp goal has established a seven-point advantage over the bottom two.
With at least one match in hand on many of their nearest rivals, Kelly will recognise that there is a window of opportunity to establish some breathing space ahead of the run-in.
That said, Barrow can ill-afford a setback on Tuesday night with defeat providing Grimsby with the boost that they desperately need at this stage of the campaign.
Having posted just one success since December 22, few people are giving the Mariners any chance of avoiding relegation to the fifth tier of English football.
Nevertheless, a double-header with Barrow and 20th-placed Walsall provides Paul Hurst and his team with the chance to get back into contention for survival.
Four stalemates in succession suggests that Hurst is beginning to have an effect on a group of players who have been struggling for confidence since the turn of the year.
Grimsby earned their 2-2 draw at Mansfield Town at the weekend courtesy of a late equaliser, providing this team with some momentum ahead of the long trip to Holker Street.
Barring any late fitness issues, Kelly may opt to select the same starting lineup from the dramatic win over Mansfield.
Having been introduced as a late substitute before netting the winner, Taylor will feel that he could be recalled in place of Bradley Barry.
Williams will almost certainly be provided with a start for Grimsby after contributing a goal and an assist during his second-half outing at the weekend.
Barrow possible starting lineup:
Dixon; Jones, Davies, Thomas; Eardley, Barry, Taylor, Banks, Brough; James, Quigley
Grimsby Town possible starting lineup:
McKeown; Hendrie, Waterfall, Hewitt, Clifton; Lamy, Matete, Coke, Jackson; Williams, John-Lewis
We say: Barrow 2-1 Grimsby Town
While there is an argument that Grimsby would welcome a draw, Hurst is aware that his side are running out of games to make headway up the table. Nevertheless, with Barrow having impressed in recent games, we can see the home team edging this fixture by the odd goal in three.