The visitors arrived at Cappielow on the back of only one defeat in 10 matches but Allan Moore's men squeezed past them 2-1.
Martin Hardie contributed the opening goal after Livingston goalkeeper Andy McNeil was left unprotected at a15th-minute corner kick. Livingston matched the home side for long spells, however, and in Marc McNulty they had a player of genuine threat.
It was no surprise when Iain Russell's accurate left boot came up with an equaliser eight minutes into the second half, but Peter MacDonald's back-post header from Michael Tidser's free-kick midway through the second half proved decisive.
Partick Thistle registered their first victory in five games with a handsome 4-1 win over Falkirk at Firhill. Conrad Balatoni and Chris Erskine each scored twice. Falkirk will feel the final scoreline flattered the home side, but the roof rather caved in when Thistle scored twice in a five-minute spell midway through the second half.
Balatoni built the foundations when he headed in a Ross Forbes corner after barely three minutes, but the prolific Lyle Taylor equalised with a precise finish in the 18th minute.
That stirred Partick into an immediate response, Erskine putting them back in front with a header from close range. Scott Fox produced an instinctive save to deny the striker soon afterwards as Falkirk caused Thistle some problems on the break. However, Michael McGovern in the away goal was equally busy, leaping across to keep out a well-struck effort from Sean Welsh.
McGovern then denied Steven Craig at one end while Taylor missed a glaring opening at the other. It was left to defender Balatoni to put Thistle further ahead after 62 minutes and before Falkirk could respond Erskine scored a wonderful fourth goal when he spotted McGovern off his line and lofted the ball into the net.
Dumbarton won their fourth game in five by edging out Airdrie United 2-1 away from home to pull level with their opponents and Cowdenbeath on 17 points at the bottom. Ryan Donnelly put Airdrie in front but Dumbarton came back to win thanks to goals from Marc McCusker and Jim Lister.
Hamilton Academical stung Raith Rovers with a late double to win 2-0 at Stark's Park in a match that saw the home side's Dougie Hill collect a third red card of the season late in the game.
Hamilton's Steven May was denied on a couple of occasions by David McGurn in the first half. Allan Walker should have put Raith in front after he was tripped in the area by Martin Canning, but his penalty was saved by Kevin Cuthbert.
Hill was shown a straight red for a two-footed lunge on Darian McKinnon before Hamilton edged in front after 88 minutes with a Brian Graham own goal. May made sure of the points with an injury-time free-kick.