Thistle dropped out of the promotion race with a disappointing home defeat to Mayfield & Easthouses.
Despite the majority of the possession and opportunities, the hosts were unable to break down the resolute rearguard of the visitors.
Mayfield took a two goal lead just after the second half but the Linlithgow men rallied and responded well, gaining a goal back from a diving G Deans header from a neat Taylor freekick.
However, Thistle were unable to claim an equaliser, meaning the visitors require Cramond to drop points against Penicuik in the final match next Saturday to clinch promotion.
Thistle face local rivals Bathgate Thistle in their final match of the season on Wednesday.