A visible astrocomb spanning 555-890 nm has been implemented on the 10-m Southern African Large Telescope, delivering complete calibration of one channel of its high-resolution spectrograph and an accurate determination of its resolving power. A novel co-coupling method allowed simultaneous observation of on-sky, Th-Ar lamp and astrocomb channels, reducing the wavelength calibration uncertainty by a factor of two compared to that obtained using only Th-Ar lines. The excellent passive stability of the master frequency comb laser enabled broadband astrocomb generation without the need for carrier-envelope offset frequency locking, and an atomically referenced narrow linewidth diode laser provided an absolute fiducial marker for wavelength calibration. The simple astrocomb architecture enabled routine operation by non-specialists in an actual telescope environment. On-sky spectroscopy results are presented with direct calibration achieved entirely using the astrocomb.