The Irish defender struck eight minutes from time after Danny Livesey looked to have put the hosts on course for victory with a headed opener three minutes earlier.
Bluebirds forward Jordan Williams came closest to breaking the deadlock in a tight first half, firing his first opportunity over the crossbar before being denied by Macc goalkeeper Scott Flinders minutes later.
Barrow, who were eight games unbeaten going into the game, eventually edged in front when captain Livesey rose to nod in Williams' 79th-minute cross.
But they were denied all three points as Byrne grabbed his first goal of the season.
Report supplied by the Press Association
Match ends, Barrow 1, Macclesfield Town 1.
Second Half ends, Barrow 1, Macclesfield Town 1.
Liam Hughes (Barrow) is shown the yellow card.
Substitution, Macclesfield Town. Jack Mackreth replaces Jack Sampson.
Goal!  Barrow 1, Macclesfield Town 1. Neill Byrne (Macclesfield Town).
Goal!  Barrow 1, Macclesfield Town 0. Danny Livesey (Barrow).
Substitution, Barrow. Andy Haworth replaces Richard Bennett.
Second Half begins Barrow 0, Macclesfield Town 0.
First Half ends, Barrow 0, Macclesfield Town 0.
First Half begins.
Lineups are announced and players are warming up.

Calais officials said the man was "crushed" by pallets and was found by a Hungarian driver at about 07:00 BST.
The Iraqi man was travelling with two other family members, who were unhurt, a spokesman for the Prefecture du Pas de Calais said.
He is the 12th person to have died trying to cross the English Channel to reach Britain since late June.
Last week, a teenager, thought to be from east Africa, was killed by a freight train near the Channel Tunnel entrance in Calais.
Days earlier a man died when he was electrocuted at the tunnel entrance.
The situation in Calais is part of a wider migrant crisis across Europe, with huge numbers of people heading north from the Mediterranean.

Rochdale's Joe Bunney broke the deadlock, netting from six yards before Nathaniel Mendez-Laing doubled the lead against his old club from close range.
Michael Smith then halved Posh's deficit from 25 yards 10 minutes before half time.
Rochdale's Bunney and Posh's Chris Forrester both saw second-half efforts well saved as the Dale held on.
The result ends Peterborough's play-off hopes, with Posh sitting 14 points outside the top six, while Rochdale keep their slim play-off hopes alive, with seven points separating them and the top six.
Rochdale Manager Keith Hill told BBC Radio Manchester:
Media playback is not supported on this device
"We're still chasing the dream, it's a massive dream but the players have stood up to the challenge.
"The recent form is absolutely superb and I'm really pleased with today's performance.
"Our attitude, our grit, our determination in the second half to keep the second half clean sheet was magnificent."
Neill Byrne bundled home a late equaliser as Macclesfield rescued a draw at fellow National League high-flyers Barrow.
[NEXT_CONCEPT]
A 20-year-old Iraqi has been found dead in a UK-bound lorry in Calais port, French authorities have said.
[NEXT_CONCEPT]
Peterborough were narrowly beaten by Rochdale as all three goals came in the first half at the ABAX Stadium.