Vertical Federated Learning (VFL) enables collaborative model training across feature-partitioned devices, yet its reliance on device-server information exchange introduces significant communication overhead and privacy risks. Downlink communication from the server to devices in VFL exposes gradient-related signals of the global loss that can be leveraged in inference attacks. Existing privacy-preserving VFL approaches that inject differential privacy (DP) noise on the downlink have the natural repercussion of degraded gradient quality, slowed convergence, and excessive communication rounds. In this work, we propose DPZV, a communication-efficient and differentially private ZO-VFL framework with tunable privacy guarantees. Based on zeroth-order (ZO) optimization, DPZV injects calibrated scalar-valued DP noise on the downlink, significantly reducing variance amplification while providing equivalent protection against targeted inference attacks. Through rigorous theoretical analysis, we establish convergence guarantees comparable to first-order DP-SGD, despite relying solely on ZO estimators, and prove that DPZV satisfies $(ε, δ)$-DP. Extensive experiments demonstrate that DPZV consistently achieves a superior privacy-utility tradeoff and requires fewer communication rounds than existing DP-VFL baselines under strict privacy constraints ($ε\leq 10$).