Two opportunist goals from Graham Dorrans set up Livingston for a comfortable Scottish Cup win. He hit his first after 30 minutes when he tapped in a Joel Hamill cross before James McArthur fired in an equaliser.
Steven Tweed headed Livi's second after from a Daryl Filley free-kick and Joe Hamill volleyed in their third.
Dorrans netted his second when he dispossessed Tony Stevenson and rounded the keeper, while 16-year-old James McCarthy netted a consolation goal.
Hamilton Accies: Jellema, Wilson (Gilhaney 46), Stevenson, Easton, Gibson, McCarthy, McArthur, Neil, Winters (McJimpsey 70), McLeod, Wake (Taylor 70). Subs Not Used: Sharp, White.
Booked: Neil, Gilhaney. Goals: McArthur 54, McCarthy 86.
Livingston: Wight, MacKay, McPake, Tweed, Miller, Walker, Smylie, Mitchell, Hamill, Craig (Shields 58), Dorrans (Snodgrass 82). Subs Not Used: Griffiths, Torrance, Monteith.
Booked: Walker. Goals: Dorrans 30, Tweed 65, Hamill 73, Dorrans 81.
Att: 1,228
Ref: D McDonald