Hamilton completely dominated the first half, accumulating nine corners in a 20-minute spell with the Lions struggling to play the ball out of their own half.
The away side should have been in front after only 13 minutes of play but Colin Stewart displayed superb reflexes to deny David Winters for notching his first goal in the hoops of Hamilton.
Five minutes later Livi had their hearts in their mouths. Richard Offiong, who was inspirational leading the Lanarkshire line, managed to beat the offside trap and race in on goal.
Stewart raced out to smother the Englishman's effort but the ball trickled temptingly towards the empty net. Dave McKay popped up with only inches to spare, knocking the shot to safety.
Hamilton managed to take the lead just before half-time with the home defence caught napping. James McArthur played a superb defence-splitting pass for Mark Gilhaney to approach menacingly on goal.
The diminutive winger showed great poise to deftly clip the ball over the helpless Stewart.
Livingston displayed more aggression in the second half but struggled to break down a resolute Accies defence.
Jason Thomson had the best chance for the home side but the defenders wayward cross did not fool Raymond Jellema in the Hamilton goal.