Five Socceroos started at Easter Road in Lewis Miller and Martin Boyle for Hibs and Kye Rowles, Calem Nieuwenhof and Nathaniel Atkinson for Hearts, while former Central Coast Mariners coach Nick Montgomery also had Australian Jimmy Jeggo on the Hibs bench.
The game looked on course to end goalless after both Shankland and Boyle missed early penalties.
But the talismanic Jambos skipper sparked jubilation among the visiting support in the 93rd minute when he notched his 44th goal in 18 months and 16th of the season to secure a third consecutive clean-sheet victory for the Tynecastle side.
"His (Shankland) goal return is unbelievable ... his hold-up play now, his standing in the game is miles from where it was when he was at Ayr or Dundee United," Hearts boss Steven Naismith said.
"He is now a leader, he is the captain. He is an all-round centre-forward who I would argue is now the best finisher in Scotland."
Hearts were handed the chance to open the scoring in the fifth minute when they were awarded a penalty following a VAR review after Rocky Bushiri was deemed to have handled the ball. Shankland saw his low strike the outside of David Marshall's right-hand post.
Hibernian then won a spot kick in the 14th minute after Dylan Vente's goalbound shot was blocked by the flailing hand of Rowles. However, Zander Clark did superbly to get down to his right and push Boyle's effort onto the post.
Rowles made a couple of crucial blocks before Hearts substitute Kenneth Vargas fired just over in the 68th minute.
Marshall then thwarted Shankland but the Jambos captain was not to be denied and curled home a clinical, match-winner after finding himself space in the box following a long ball from Clark.
"It's a cruel game at times," Montgomery said.
"Both teams would probably have been happy with a draw, but it's one moment of quality.
"It's a quality strike and it's why there's so much in the media about him (Shankland) moving on. He's one of the best strikers in the league and, apart from that one moment, we did keep him quiet."
Earlier in the day, games at Ibrox and Pittodrie were postponed after extreme weather conditions caused travel problems in the north of Scotland.
Rangers saw their home game against Ross County called off as snow prevented the visitors travelling south, meaning they will go into Saturday's Glasgow derby at Celtic Park five points behind the leaders with two games in hand.
Motherwell got to Aberdeen early but many supporters of both clubs were stuck as roads were closed because of flooding in the northeast.
Elsewhere, Socceroo Keanu Baccus' fifth-placed St. Mirren were beaten 1-0 by fourth-placed visitors Kilmarnock and St. Johnstone drew 0-0 at home with bottom-placed Livingstone.
