Systematic Rabi-amplitude and detuning errors remain important sources of infidelity in high-fidelity quantum gates. We develop a robust pulse-engineering scheme for non-adiabatic holonomic quantum computing in a three-level $\Lambda$-type qutrit, combining inverse engineering with time-dependent perturbative analysis. Pulse shaping eliminates the leading second-order Rabi-amplitude contribution, while static detuning introduces a distinct population-mediated channel that cannot be removed within a single control loop. We therefore introduce a compensation loop that exactly cancels the dominant second-order $O_{13}^{\delta }$ contribution, with the residual $O_{12}^{\delta }$ channel further suppressed by pulse shaping. Using the logical average gate fidelity over the complete computational subspace, the optimized composite sequence reaches closed-system fidelities of $99.88\%$–$99.99\%$ for four representative single-qubit gates at $ϵ=0.2$ and $\delta /2\pi =2$ MHz. With phenomenological decoherence at $T_1=T_2=30~\mu{\rm s}$, the NOT and S gates retain fidelities of $99.72\%$ and $99.79\%$, respectively, with a coherence-time crossover near $0.58~\mu{\rm s}$. These results identify the regime in which systematic-error suppression outweighs the decoherence cost of the additional control loop.