Rauf Aliyev scored a screamer to give the Group F minnows a fifth-minute lead and Northern Ireland conspired to waste at least half a dozen glorious chances to equalise.
Craig Cathcart and Chris Baird spurned four of the best between them and it took Healy's first goal in four years, deep in added time, to avert what would have been an embarrassing defeat.
The result leaves Northern Ireland with three points from four games and all but out of the reckoning, as well as consigning last month's heroic draw in Portugal firmly to the history books.
The home side began positively and should probably have taken a third-minute lead when Niall McGinn floated over a precise cross for Kyle Lafferty, who somehow headed over from just six yards.
That miss was punished within 90 seconds as Azerbaijan took a surprise lead with their first attack. Javid Huseynov won the ball in midfield and laid off to Aliyev, who bent in a stunning shot from 30 yards before embarking on ecstatic celebrations.
Northern Ireland, meanwhile, were enjoying plenty of time on the ball but struggling to make the final pass count. McGinn worked rookie goalkeeper Salahat Aghayev with a first-time shot from the edge of the area and Dean Shiels played an inviting ball across the face of goal but Azerbaijan survived unscathed on both occasions.
After 26 minutes Steven Davis chipped a fine ball over the back four to give Kyle Lafferty a one-on-one attempt but a loose first touch allowed Aghayev to smother. Another gilt-edged chance came and went on the half-hour, Dean Shiels finding Cathcart with a cushioned header across goal and the Blackpool defender nodding wide from a wonderful position.
The equaliser almost arrived just two minutes into the second period. Gareth McAuley nodded down Steven Davis' free-kick and Cathcart controlled the ball on his chest before blazing over from the six-yard line. Chances continued to flow and on the hour mark, Baird produced arguably the worst miss yet, heading Shane Ferguson's cross wide at the far post when scoring seemed easier.
Michael O'Neill played his final card by sending on Healy for Cathcart. It looked like even that would not be enough but five minutes into a generous period of injury time, the fan favourite drilled home a free-kick to rescue a dramatic point. That is unlikely to be enough to rescue Northern Ireland's slim qualifying hopes but it did save his side from one of their most ignominious defeats.
Source: PA
Source: PA