Clyde had the ball in the net early on as Dougie Imrie troubled the visiting defence but the goal was chalked off by the referee for an earlier infringement.
The Broadwood men's sharp passing was proving tricky for the Livingston defence and Joe Miller's side looked particularly dangerous at set-pieces.
But it wasn't until just after the re-start that Clyde finally capitalised on their early good play with Andy Ferguson scoring after Paul McHale's effort had led to a corner for Clyde.
Livingston began to lift their game after going behind with substitute Shields seeing his effort blocked on the line.
The equaliser eventually came with five minutes remaining when Steve Hislop flicked the ball on to Shields who headed in from close range.
But the match ended on a sour note for Livi when Steven Craig was sent off for picking up his second yellow card of the match.
The result leaves Livingston in second place in the table, level on points with table-topping Gretna and third-placed St Johnstone while Clyde remain in seventh place.