Proton tunneling through a hydrogen bond is a significant quantum phenomenon in proton-mediated processes. Hydrogen bonds strengthen each other through cooperative interactions, enhancing proton tunneling. Controlling cooperativity of the hydrogen-bond network is required to understand the role of cooperativity in proton tunneling; however, engineering hydrogen bonds is difficult due to the stable structure of hydrogen-bonded cluster. Here, we demonstrate that collective proton tunneling can be controlled inside a cyclic water trimer simply by assigning an asymmetry in the adsorption structure. Asymmetric configuration of water trimers in registry with the NaCl(001) surface perturbs the strength of hydrogen bonds, destroying cooperativity. We reveal two pathways that facilitate proton tunneling in the interfacial trimer: vibration-excited and rotation-mediated processes. The vibrationally excited states lead to lowering the tunneling barrier, and the intermolecular rotation increases the cooperativity by modifying the adsorption configuration. Our results highlight the atomic-scale control of hydrogen bonds, which is crucial in proton-involved reactions.