Manager Lee Bradbury named the same starting line-up that lost 2-1 at Eastleigh on New Year’s Day.
Before the game, a presentation was made to captain Brian Stock, who was retiring to take up a coaching role with AFC Bournemouth.
A quick early break by the visitors ended with Jack Barthram slicing a shot over the bar.
At the other end, Bradley Tarbuck robbed Dan Jones to set up a chance for the Hawks, but Alfie Rutherford’s effort was blocked.
Ominously, Barrow started to take charge – particularly in midfield as the half-hour mark approached.
Yet the home side finished the half the stronger, and as the interval approached Tyler Frost and Ryan Woodford both went close inside a minute.
With just the goalkeeper to beat, Frost saw his shot turned behind for a corner.
From the resulting flag-kick, Woodford sent a header crashing off the top of the crossbar.
Then Andreas Robinson and Frost both failed to score from good positions before the break.
Barrow’s Raek McFarlane had a great chance at the start of the second half but shot weakly at home keeper Ben Dudzinski.
But it was the Hawks who broke the deadlock on 55 minutes, after Rutherford linked with Tarbuck on the right.
Tarbuck curled in a cross and Theo Lewis stooped to head into the net at the far post.
The visitors had the ball in the net soon afterwards, but McFarlane was adjudged to have handled the ball.
Then, when Barrow next attacked, Rhys Norrington made a horrible mess of his cross.
Lewis came to the Hawks’ rescue with a goal-line clearance following a corner.
The visitors then had Kyle Jameson sent off 10 minutes from the end after he led with his arm in a challenge on Lewis.
Williams sealed the win in stoppage-time with a tremendous long-range strike