We present a driving scheme for solid-state quantum emitters, referred to as Notch-filtered Adiabatic Rapid Passage (NARP), that utilizes frequency-swept pulses containing a spectral hole resonant with the optical transition in the emitter. NARP enables high-fidelity state inversion and exhibits robustness to variations in the laser pulse parameters, benefits that are derived from the insensitivity of the condition for adiabatic evolution. NARP also offers the advantage of immunity to phonon-mediated excitation-induced dephasing when positively chirped control pulses are used. Our resonant driving approach could be combined with spectral filtering of the scattered pump light and photonic devices for enhanced collection efficiency to realize simultaneous high indistinguishability and brightness in single photon source applications.