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 inside 90 minutes.
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.
Burnley left-back Danny Lafferty earned a competitive debut after Ryan McGivern failed a fitness test.
The home side began positively and should 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.
Azerbaijan looked dangerous on the counter-attack and only a Gareth McAuley block denied Aliyev the chance to try his luck a second time.
Chance after chance went begging for the Irish before former Leeds United striker Healy snatched a dramatic point after drilling home a free kick.
Andrija Delibasic scored twice as Montenegro knocked England off the top of the World Cup Qualifying Group H with a 3-0 victory over group minnows San Marino in Podgorica.
Delibasic opened the scoring after 14 minutes and made it 2-0 at the break when he doubled the home side’s lead on the half-hour. Elsad Zverotic added the third in the second half.