In the field of quantum metrology, transition matrix elements are crucial for accurately evaluating the black-body radiation shift and the parity-violating amplitude of the clock transition, and can be used as probes to test quantum electrodynamic effects, especially at the $10^{-3}$-$10^{-4}$ level. We developed a universal experimental approach to precise determination of the dipole transition matrix element with a energy level of two transition channels at various atomic species by using the quantum shelving technique. In which, the time-increased pulses were utilized to induce quantum shelving, and the resulting shelving probabilities were determined by counting the scattered photons from the excited $^{2}\!P_{1/2}$ state to the $^{2}\!S_{1/2}$ ground state. Using the scattered photons offers several advantages, including insensitivity to fluctuations in magnetic field, laser intensity, and frequency detuning. An intensity-alternating sequence to minimize detection noise and a real-time approach for background photon correction were implemented in parallel. We applied this method to single Yb$^+$ ion, and determined the $6p~^{2}\!P_{1/2}$ - $5d~^{2}\!D_{3/2}$ transition matrix element of 2.9395(21)~$ea_{0}$, which represents an order of magnitude improvement over previous determination. By combining our result with the $6p~^{2}\!P_{1/2}$ lifetime of 8.12(2)~ns, we extracted the $6s~^{2}\!S_{1/2}$ - $6p~^{2}\!P_{1/2}$ transition matrix element to be 2.4695(31)~$ea_{0}$.