We focus on the impacts of technological spillovers and environmental awareness in a two-echelon supply chain with one-single supplier and one-single manufacturer to reduce carbon emission. In this supply chain, carbon abatement investment becomes one of key factors of cutting costs and improving profits, which is reducing production costs in the components and products—the investment from players in supply chain. On the basis of optimality theory, the centralized and decentralized models are respectively established to investigate the optimal decisions and profits. Further, setting the players’ profits of the decentralized scenario as the disagreement points, we propose a bargaining-coordination contract through revenue-cost sharing to enhance the performance. Finally, by theoretical comparison and numerical analysis, the results show that: (i) The optimal profits of players and supply chain improve as technological spillovers and environmental awareness increase, and the profits of them in the bargaining-coordination contract are higher than that in the decentralized scenario; (ii) Technological spillovers between the players amplify the impact of “free-ride” behavior, in which the supplier always incentives the manufacturer to improve carbon emission intensity, but the cooperation will achieves and the profits will improve only when technological spillovers and environmental awareness are great; (iii) The contract can effectively achieve coordinated supply chain, and improve carbon abatement investment.