The 18-year-old, on loan at Clydebank last season, was pitched into the line-up due to the unavailability of Lee Hodson, who is required to undergo a period of isolation after his housemate, St Mirren's Jak Alnwick, tested positive for Covid-19.
Munro only made his debut a fortnight ago as a late substitute against Rangers yet never looked out of his depth against the Lions and emerged as the unlikeliest of heroes.
He clinically headed home at the back post in the dying embers to secure a smash-and-grab triumph after David Templeton had cancelled out Shaun Want's early own goal.
Their second win of the campaign saw Hamilton, perennial relegation favourites, leapfrog Livi and move into ninth spot in the Premiership.
It was an outcome which appeared unlikely with just 29 seconds on the clock.
Lars Lokotsch linked up superbly with Alan Forrest, sending the winger scampering into the box, and his low cross was turned into the net via a combination of Scott Pittman and sliding Accies skipper Want. The latter got the inadvertent final touch.
Visiting goalkeeper Ryan Fulton made a sharp sprawling save to deny Forrest as Livi dominated.
Marvin Bartley then headed into the arms of the Accies number one from point-blank range following a goal-mouth scramble.
Templeton was the only man in blue carrying any semblance of threat in the first period, with a low free-kick from 20 yards that fizzed wide of the post representing the best Hamilton could muster.
However, Brian Rice's charges were a different team in the second half and swiftly levelled through that man Templeton.
Hakeem Odoffin met a Reegan Mimnaugh corner and struck the crossbar with a thundering header, only for the ex-Hearts and Rangers player to lash home the rebound.
Templeton, in irrepressible mood in West Lothian, then curled a terrific effort tantalisingly wide following a fine Cruyff turn on the edge of the Livi box.
Livingston blew a golden chance to reclaim the lead when Pittman struck the under-side of the bar from six yards following a Craig Sibbald knock-down.
And Accies made them pay by stealing all three points in the dying embers, with Munro ghosting in to meet a Templeton free-kick and coolly nod beyond Robby McCrorie.