Because of the advantages of strong robustness and good scalability, TWSNs (two-tiered wireless sensor networks), which are known as parts of the IoT (Internet of things) observation systems, attract more and more attention. However, many security problems have not yet been well solved in TWSNs. In hostile environments, the adversaries are prone to illegally obtain the information stored on the master nodes, which are known as the key nodes of TWSNs, and even destroy the integrity of the query results returned to Sink node by capturing the master nodes and making them malicious. In this paper, we focus on the problem of privacy-and-integrity preservation for Top-k queries in TWSNs and propose a secure query-processing protocol named VPP (verifiable privacy-and-integrity preservation). Based on the OPES (order preserving encryption scheme), the SC (symmetric ciphering) and the weight binding techniques, VPP achieves privacy-and-integrity preservation for Top-k queries by specifying the data preprocessing mechanism at the sensor nodes, the Top-k query-processing mechanism at the storage nodes, and the integrity-validating method at Sink node. Both theoretic analysis and simulation results show that VPP outperforms the state-of-the-art scheme on not only the security but also the energy efficiency of Top-k query processing in TWSNs with reasonable computation complexity.