Shep Murombedzi's 25-yard deflected effort put the hosts into the lead midway through the opening half, but the goalscorer then brought down Danny Rowe in the box and Kingsley James converted from the spot.
Solihull were then handed a spot-kick of their own on the stroke of half-time when the visitors were penalised for tugging, and Akwasi Asante slotted home from 12 yards.
James took his goal tally for the season to four with his second penalty three minutes after half-time.
He was tripped in the box by Jamie Osborne but picked himself up to level the scores before Norburn won it at the death.
Report supplied by the Press Association.
Match ends, Solihull Moors 2, Macclesfield Town 3.
Second Half ends, Solihull Moors 2, Macclesfield Town 3.
Goal!  Solihull Moors 2, Macclesfield Town 3. Ollie Norburn (Macclesfield Town).
Substitution, Solihull Moors. Ryan Beswick replaces Shepherd Murombedzi.
Omari Sterling-James (Solihull Moors) is shown the yellow card for a bad foul.
Substitution, Macclesfield Town. Chris Holroyd replaces Jack Sampson.
Jack Byrne (Solihull Moors) is shown the yellow card for a bad foul.
Paul Lewis (Macclesfield Town) is shown the yellow card for a bad foul.
Substitution, Solihull Moors. Stefan Moore replaces Harry White.
Substitution, Solihull Moors. Omari Sterling-James replaces Darryl Knights.
Jamey Osborne (Solihull Moors) is shown the yellow card for a bad foul.
Substitution, Macclesfield Town. Danny Whitaker replaces Kingsley James.
Goal!  Solihull Moors 2, Macclesfield Town 2. Kingsley James (Macclesfield Town) converts the penalty with a.
Second Half begins Solihull Moors 2, Macclesfield Town 1.
First Half ends, Solihull Moors 2, Macclesfield Town 1.
Goal!  Solihull Moors 2, Macclesfield Town 1. Akwasi Asante (Solihull Moors) converts the penalty with a.
Goal!  Solihull Moors 1, Macclesfield Town 1. Kingsley James (Macclesfield Town) converts the penalty with a.
Shepherd Murombedzi (Solihull Moors) is shown the yellow card for a bad foul.
George Pilkington (Macclesfield Town) is shown the yellow card for a bad foul.
Substitution, Macclesfield Town. Dan Cowan replaces John McCombe.
Goal!  Solihull Moors 1, Macclesfield Town 0. Shepherd Murombedzi (Solihull Moors).
First Half begins.
Lineups are announced and players are warming up.
Ollie Norburn's last-gasp goal saw Macclesfield end Solihull's unbeaten home run with a thrilling victory which featured three penalties in the space of seven minutes.