Increasing use of natural gas for electricity production places added strains on pipeline systems that are used for transporting fuel. Pipeline constraints require power system operators to account for natural gas-supply restrictions in their operational processes. This paper proposes separate optimization models for clearing day-ahead wholesale markets for scheduling power and natural gas systems. We then develop a market-based mechanism that allows for efficient co-ordination of the two systems. Importantly, the co-ordination mechanism only requires the exchange of fuel-price, -supply, and -demand information between the two markets. This can be contrasted with other co-ordination mechanisms that require operations of the two systems by a single entity. Thus, we provide a computationally tractable co-ordination mechanism that does not require the exchange of proprietary information between natural gas and electricity system operators. We demonstrate the effectiveness and scalability of the technique using a numerical example.