The key to realizing fault‐tolerant quantum computation for singlet‐triplet (ST) qubits in semiconductor double quantum dot (DQD) is to operate both the single‐ and two‐qubit gates with high fidelity. The feasible way includes operating the qubit near the transverse sweet spot (TSS) to reduce the leading order of the noise, as well as adopting the proper pulse sequences which are immune to noise. The single‐qubit gates can be achieved by introducing an AC drive on the detuning near the TSS. The large dipole moment of the DQDs at the TSS has enabled strong coupling between the qubits and the cavity resonator, which leads to two‐qubit entangling gates. When operating in the proper region and applying modest pulse sequences, both single‐ and two‐qubit gates have fidelity higher than 99%. The results in this paper suggest that taking advantage of the appropriate pulse sequences near the TSS can be effective to obtain high‐fidelity ST qubits.