Healy was given a special award by UEFA president Michel Platini before the Windsor Park match in honour of his scoring exploits in Euro 2008 qualifying, but he missed a string of chances before Burnley striker Kyle Lafferty finished a snappy move for the opener.
Healy did register with a deflected long-range shot before Lafferty headed a third, his second, as the hapless Georgians capitulated before the break.
Nigel Worthington's team lost momentum badly after the break following a string of substitutions, and Healy slid the ball into his own net after Maik Taylor had saved Levan Tskitishvili's spot-kick following a handball by debutant Michael O'Connor.
Peter Thompson looked to have bundled in a late fourth for the hosts, but it went down as a Levan Kobiashvili own goal.
The home side dominated from the off. Veteran winger Keith Gillespie broke free down the right flank in the second minute and crossed low across the face of goal, but none of the on-rushing attackers were able to make contact with his dangerous ball.
Healy almost made it 34 international goals in the 15th minute when Georgia goalkeeper George Makaridze spilled a cross from the recalled Stuart Elliott, but he atoned for his error to save the striker's mis-hit follow-up effort.
Moments later Healy turned and sent a dipping 20-yard shot just past the post before yet another shot was well blocked after good work from Gillespie.
Healy got on to a bouncing ball that eluded the defence to fire in another effort from the edge of the area, which was straight at Makaridze.
The home side were utterly dominant and fashioned a classy opening goal in the 25th minute after the Georgians gave the ball away in defence.
Healy fed Steven Davis, who squared for Kyle Lafferty to score his fourth international goal with a first-time shot from 10 yards.
Taylor saw his first action of the night in the 32nd minute when he was forced to punch clear Alexander Iashvili's shot from an acute angle.
But it was two a minute later when Healy latched on to Damien Johnson's header and shot from 25 yards.
A wicked deflection off AC Milan defender Kakha Kaladze was enough to send it past the sprawling Makaridze.
Lafferty then made it three in the 36th minute with a fine header from Healy's right-wing cross.
It was the second match in succession that the Georgians - ranked 76th in the world by FIFA - had found themselves three down at the interval following their 3-1 defeat by Latvia in Tbilisi last month.
Crewe midfielder O'Connor came on for his debut at the start of the second half, with Warren Feeney also joining the action as Johnson and Lafferty made way.
Georgia's Levan Kenia tried his luck from 20 yards in the 50th minute but his shot was well wide, before Davis clipped into the side-netting from a tight angle.
Then, out of nowhere, the visitors won a penalty in the 54th minute when O'Connor handled a cross.
Taylor made a brilliant save low to his right to tip Tskitishvili's spot-kick on to the post, and as the midfielder attempted to collect the follow-up, Healy slid in to challenge but only succeeded in sending the ball into his own net.
Gareth McAuley was sent on for Stephen Craigan as manager Worthington attempted to shore up his suddenly stretched defence.
A smartly worked free-kick in the 69th minute ended with Healy firing a 25-yard shot that was comfortably saved by Makaridze.
It was Healy's last action as youngsters Michael Gault and Peter Thompson were brought on, Davis also making way.
Taylor then made a smart parry from Iashvili's close-range shot and fingertipped Kobiashvili's diagonal shot to safety.
At the other end, Feeney curled wide from a good position after some slack defending.
Alan Mannus became the third Linfield player to be brought on, after Thompson and Gault, when he replaced Taylor in goal.
In the 87th minute, Thompson bundled home a fourth for Northern Ireland - arguably with his arm - after Aaron Hughes' flick-on caused panic in the Georgian defence.