Livi's 2-0 win over their nearest challengers came courtesy of goals from Dale Carrick and Nicky Cadden.
Brechin City moved above Alloa Athletic and to within a point of second place by beating Stranraer, with the Wasps drawing with Queen's Park.
East Fife won Barry Smith's first match in charge against Peterhead and bottom side Stenhousemuir beat Albion Rovers.
Carrick's shot gave Livi an early lead at home to the Diamonds and Cadden's late strike sealed the win for David Hopkin's side.
At Glebe Park, Ally Love fired Brechin ahead on the quarter-hour and that lead was doubled by Connor McLennan's free-kick before half-time.
Stranraer had Steven Bell sent off in the second half for two bookings.
Queen's Park went ahead away to Alloa through Ross Millen's 62nd-minute shot, but the hosts were level within seven minutes through Greig Spence's strike.
The Fifers moved out of the bottom two after scoring two second-half goals against Peterhead, Jason Kerr then Kevin O'Hara firing in.
Smith's side were replaced in ninth by Stranraer, who are only two points ahead of Stenny.
Willis Furtado's strike gave the Ochilview side a narrow home win.

Musgrove Park Hospital said the cause of the "technical issues" in the hired facility was being investigated.
Surgery was carried out on 62 patients with just under half reporting complications while some 15 people had "more significant" corneal issues.
The use of the mobile facility was ceased when the issues were discovered.
All affected patients have been spoken to and care plans are now in place for their ongoing treatment, a hospital spokesperson said.
Vanguard Healthcare had been hired to provide the theatre to help clear a backlog for some ophthalmic services.
The unit, which consists of an anaesthetic room, operating theatre and two-bed recovery, is at the hospital until the end of the year.
Vanguard said it was "co-operating fully" with the hospital for the investigation which would focus on the drugs, equipment, sterilisation and protocols used.
"The majority of operations were successful, however a number experienced an unusual level of discomfort after surgery," added a spokesperson.
"We have, with the hospital, conveyed to the patients our concern and sympathy for the discomfort or distress they have experienced."
The hospital's chief executive, Jo Cubbon, said the issues meant many patients who had already waited longer than they should have, will now have to wait again for their operation.
"We are very sorry this has happened and are working to put a solution in place so that these patients will receive their treatment as soon as possible," Ms Cubbon said.

Judges scored four restaurants selected to represent each town or city, assessing hygiene ratings and public votes.
The West Yorkshire city was praised for holding several curry-themed events, including a poppadom-eating challenge.
Glasgow finished second and Brighton came in third in the competition, which marks the end of National Curry Week.
Leicester and Birmingham finished fourth and fifth respectively.
The restaurants selected to represent Bradford were Aakash, Kiplings, Shimla Spice and Akbar's.
Patricia Tillotson, of Visit Bradford, said: "Winning the hotly-contested competition this many times in a row has never been done before.
"Our entry has created a real sense of community cohesion, which ultimately is what the Curry Capital of Britain competition is all about."
Our love affair with curry
See: BBC Food - Curry recipes
The curry capital title was first awarded in 2001. It was won by Bradford in 2004 in addition to  2011-2014.
Livingston moved 10 points clear at the top of Scottish League One after beating Airdrieonians.
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About 30 patients in Somerset who had cataract surgery inside a mobile hospital theatre have been left with blurred vision or other complications.
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Bradford has been named Curry Capital of Britain for a record-breaking fifth year in a row.