One common theme in the international construction sector is project variation, which influences project outcomes. This study argued that variation could occur during the lifecycle of a construction project that might affect the contracted project success criteria (PSC), including cost, time, quality, or scope parameters. These variations can originate from the owner, consultant, contractor, or external factors. The construction industry is a critical partner in operationalizing and implementing the long-term sustainability objectives of Vision 2030 in the Kingdom of Saudi Arabia (KSA). The present study identified 18 factors that can cause variation orders by the owners of construction projects and evaluated them using statistical and fuzzy-based methods. To estimate the influence of variation orders on PSC in Saudi Arabia, over 70 experienced professionals, including project managers (58%), engineers (26%), and strategic management officers (16%) working in the construction industry evaluated the identified factors through a questionnaire survey. A 1–4 Likert scale, no impact (1) to high impact (4) on PSC, was used to rank identified factors. Analysis of variance and Tukey tests found no statistically significant difference between the respondents’ opinions. Out of the four PSC, cost and time with 14 out of 18 factors obtaining scores higher than “3” superseded quality with seven and scope with six factors. The Fuzzy Synthetic Evaluation identified inadequate planning, managerial corruption, the method of lowest bidding procurement, the inadequate experience of owner’s staff, additional work added by the owners, delayed starts, mode of financing and payments, and public works contract rigidity as the most critical factors affecting PSC of the construction projects in the view of participated stakeholders. Conversely, shortening the project period, long intervals between design and project initiation, and restrictions against foreign companies were identified as the least important factors. The study helps stakeholders achieve long-term sustainability by focusing on the top-ranked factors in KSA’s construction industry and the Gulf Region with similar working environments, rules, and regulations.