Gary Woods had given MacKinnon the chance to seal a two-point return for Accies when he saved from Scott Robinson.
But MacKinnon got his Panenka spot-kick all wrong with the 10th penalty and, after Declan Gallagher and Aaron McGowan failed to net in sudden death, Livingston goalkeeper Liam Kelly then proved the hero when he saved from Darren Lyon to earn the visitors a 6-5 penalties triumph.
The shootout provided some much-needed entertainment after an uneventful 90 minutes during which Livingston at least showed they can hold their own against top-flight opponents.
The game was initially scheduled to be played at Airdrie’s ground, but Hamilton managed to get their new artificial surface ready to host the Premiership newcomers.
Livingston had the best chance of the first half, shortly after Robinson’s shot was parried behind for a corner. The delivery eventually fell for Gallagher four yards out but the defender headed over the crossbar.
Livingston manager Kenny Miller was playing wide in a 4-1-4-1 formation but his team got pushed back for long spells of the first half. Hamilton could not trouble Kelly, though.
The visitors moved to a more familiar 3-5-2 formation in the second half with the player/manager joining Lee Miller up front but the game proved even tighter.
Rakish Bingham got Hamilton’s first effort on target in the 72nd minute but Kelly comfortably saved his header following Dougie Imrie’s free-kick. Gallagher soon threatened from a set-piece at the other end but Woods saved his header. The visitors came close to a late winner when Robinson’s long-range strike deflected off Craig Sibbald and spun just wide.
Livi move on to five points, one behind Annan, while Hamilton have one.