The club announced that director of football Collins had quit after the board sacked Evans, who replaced John Hughes as manager in November when the former Hibernian boss left for Hartlepool.
The pair leave Livingston fourth in the Irn-Bru First Division.
A club statement read: "Livingston Football Club announces the departure of first team manager Gareth Evans following a managers' meeting today, where we voiced our concern over the stewardship of the club under Gareth. This despite the results being generally acceptable.
"John Collins, having appointed Gareth to the post despite certain reservations, has regrettably decided to tender his resignation following our decision to relieve Gareth of his duties.
"First team affairs ahead of this Saturday's home fixture against Airdrie United will be handled by current Head of Youth Development, Richie Burke whilst the board consider matters going forward.
"No further comment in relation to this development will be made at this time."