Transportation is the second largest source of carbon emissions today, with more than 80% of the carbon emitted from automobile operations. Hence, reducing the fuel consumption per unit mileage while vigorously developing new energy vehicles has become an inevitable choice for carbon emission reduction. So, this paper applies the differential game approach to investigate the production trade-offs of fuel and new energy vehicles, fuel consumption reduction, and digital technology investment strategies in an automotive supply chain under a dynamic framework. In addition, it further analyzes whether the dual credit policy (DCP) can promote the healthy development of China's auto market after the withdrawal of the purchase subsidy policy for new energy vehicles (PSP). The results show that the implementation of DCP will reduce the sales of fuel vehicles with fuel consumption higher than the critical value (HFCV) but will not promote the willingness of manufacturers to invest in fuel consumption reduction of HFCV; the abolition of the PSP will not reduce the demand for fuel vehicles, nor will it affect the investment in fuel consumption reduction of fuel vehicles, but it will reduce the consumer demand for new energy vehicles. However, assuming that the government appropriately adjusts the intrinsic mechanism of the DCP, such as increasing the requirement for the proportion of new energy vehicles in the sales of cars by manufacturers and the value of the points per unit of new energy vehicles, it will be possible to promote the growth of new energy vehicles while discouraging the production of fuel-intensive vehicles. In addition, If the government abolishes PSP, the maximum rate of change in the profits of the manufacturer, retailer, and the entire supply chain in the parameter change intervals analyzed in our numerical example is only 1.6%, 0.04%, and 0.13%, respectively, which can be said to have minimal impact. The findings provide a theoretical basis for the government's choice of carbon regulation policy for the automotive supply chain.