Increasing consumers' environmental awareness has drawn more firms' attention to low-carbon production. CO2 emission management control is a critical factor in the process of low-carbon production in a supply chain. Such kind of inter-organizational control includes two different strategies: the emission control and emission reduction. Those two strategies have different influences on the performance of the supply chain. This paper uses the differential method to study the Stackelberg game between a manufacturer and a supplier in four situations: (1) the non-cooperative situation where no coordination is considered; (2) the weak incentive situation where the emission control incentive is considered; (3) the strong incentive situation where both the emission control incentive and the emission reduction incentive are considered; (4) the cooperative situation where the cooperation is considered. Optimal inter-organizational control of the emission control efforts, emission reduction efforts and cost subsidy are solved and discussed. The results show that although the emission control cost lower, its positive effect on the supply chain performance is still limited. Both the supplier and the manufacturer have the Pareto improvements from the non-cooperative situation to the cooperative situation in sequence. Finally, the simulations and sensitivity analyses are conducted to support the models. Our study provides theoretical insights to the optimal control of low-carbon production in an inter-organizational setting.