The fixture, watched by both sets of management teams as well as two Dundee United scouts, saw Martin Hardie handed a start as he begins to build up his match fitness after 11 weeks out.
David Hopkin's side took the lead in the 22nd minute when Livi defender Coll Donaldson attempted to steal possession from Lewis Hawke, but only succeeded in diverting the ball into his own net.
It was all Livi in the second period. Kyle Jacobs headed against the post while Ton keeper David Hutton made three fine stops to deny Liam Fox twice in quick succession.
Ton scored a second against the run of play in 88 minutes when Hawke laid the ball off to Aussie trialist Danny Moss. The sub's side-footed effort took a deflection off the hapless Donaldson and trundled past wrong-footed keeper Darren Jamieson.
In the last minute, Livi sub Jack Beaumont curled a sublime strike into the top right-hand corner from the edge of the box, but despite its quality, the goal proved no more than a meaningless consolation.