Simon Weaver's team went into the interval 2-0 behind having been outplayed for much of the first half, however a fortuitous Jack Muldoon strike and Callum Howe's header sealed an impressive recovery.
The opening exchanges were fairly scrappy, though Harrogate had the better of them, Muldoon seizing on a loose touch by home defender Dan Jones on the edge of his own box and firing an effort wide after three minutes.
Barrow eventually settled into their rhythm and began to ask some questions of the visiting defence, passing the ball nicely.
A hugely significant moment then arrived in the 18th minute.
A long clearance out of defence was flicked on by Mark Beck, setting Muldoon away in a foot race with Jones.
The Town striker got there first and was then taken out as he looked to accelerate clear, though referee Peter Gibbons deemed the Bluebirds man to have taken a piece of the ball.
Barrow immediately countered and a one-two between Lewis Hardcastle and Jack Hindle set the former in on goal, where he dropped his shoulder, danced around James Belshaw and rolled into an empty net.
With Weaver's men visibly reeling and gloveman Belshaw and defender Howe exchanging angry words, the home lead was doubled within four minutes.
Hindle looked to latch onto a bouncing ball into the left-hand channel and was brought down by inside the area by a rash lunge from the stretching Ryan Fallowfield.
Belshaw guessed the right way, however he couldn't get anything on the resulting spot-kick, John Rooney's low strike finding the back of the net for 2-0.
Town should have halved the arrears almost immediately when Beck got free in the box and was able to bring Warren Burrell's left-wing cross down on his chest, however he got too much on his finish and sent the ball across the face of goal and past the upright.
The remainder of the opening 45 belonged to Barrow, who were able to open up the men in yellow and black with ease as their wing-backs wreaked havoc.
James Philpot blasted over the top, then Rooney placed a strike just wide moments before the half-time whistle.
As badly as the first period went for Harrogate - who introduced Joe Leesley and Jack Senior at the interval - the second couldn't really have begun much better.
Barely 60 seconds after the resumption, the ball was rolled back to Bluebirds keeper Joel Dixon and his attempted clearance struck the advancing Muldoon then trickled into the back of the home net.
That goal out of nothing altered the momentum somewhat, and Town were suddenly in the game.
That said, it took a succession of heroic blocks inside the away box to prevent the Bluebirds from adding a third, Burell clearing off the line before various other visiting players put their bodies on the line, with Howe in the thick of it.
Jones then nodded over from close range before Weaver's troops went down the other end and levelled matters in the 69th minute.
A dreadful miss-hit back-pass by Jason Taylor led to a corner, which Leesley swung over from the left for Howe to climb and head into the bottom corner.
The closing stages saw both teams pressing for a winner, with Town's best chance coming when Muldoon raided down the left and curled one wide after his initial attempted centre to Beck was cut out.
A fifth goal of the afternoon was not forthcoming, however, and in the end the points were shared.
The result means that the Wetherby Road outfit remain sixth in the National League standings.