The Russian invasion of Ukraine in 2022 triggered a global wheat price spike and food insecurities in import-dependent countries. We combine an analysis of the global wheat supply network with an agricultural commodity price model to reproduce the global annual wheat price hike in the trade year 2022. Using a scenario analysis, we show that international cooperation manifested in the Black Sea Grain and Solidarity Lanes initiatives and the removal of export restrictions may have substantially mitigated the 2022 price hike by 13 percentage points. In a worst case scenario – characterized by multi-breadbasket harvest failures, escalating export restrictions, and blocked Ukrainian exports – wheat price increase by 90% compared to 2000–2020 average. Short-term coping strategies – such as food-secure countries dispersing stocks, reducing wheat as feed, or boosting wheat production – are effective at mitigating the price spike in simplified scenarios. Our findings emphasize the importance of internationally coordinated response measures in averting larger food crises.