gates reduces the depth of quantum circuits, streamlines quantum programming, and facilitates efficient circuit optimization, thereby enhancing overall performance in quantum computation. In this work, we propose and experimentally demonstrate a high-fidelity scheme for implementing a three-qubit controlled-controlled-Z (CCZ) gate in a flip-chip superconducting quantum processor with tunable couplers. This direct CCZ gate is implemented by simultaneously leveraging two tunable couplers interspersed between three qubits to enable three-qubit interactions, achieving an average final state fidelity of 97.94% and a process fidelity of 93.54%. This high fidelity cannot be achieved through a simple combination of single- and two-qubit gate sequences from processors with similar performance levels. Our experiments also verify that multi-layer direct implementation of the CCZ gate exhibits lower leakage compared to decomposed gate approaches. To further showcase the versatility of our approach, we construct a Toffoli gate by combining the CCZ gate with Hadamard gates. As a showcase, we utilize the CCZ gate as an oracle to implement the Grover search algorithm on three qubits, demonstrating high performance with the target probability amplitude significantly enhanced after two iterations. These results highlight the advantage of our approach, and facilitate the implementation of complex quantum circuits.