A narrow-linewidth comb-linked nonlinear source is used as master radiation to injection lock a room-temperature mid-infrared quantum cascade laser (QCL). This process leads to a direct lock of the QCL to the optical frequency comb, providing the unique features of narrow linewidth, absolute frequency, higher output power, and wide mode-hop-free tunability. The QCL reproduces the injected radiation within more than 94%, with a reduction of the frequency-noise spectral density by 3 to 4 orders of magnitude up to about 100 kHz, and a linewidth narrowing from a few MHz to 20 kHz.