Murphy pounced on a loose ball moments before half-time to score on the left after Ugo Monye failed to deal with Julien Dupuy’s hack ahead. Fly-half Toby Flood added the conversion to three earlier penalties.
Nick Evans also kicked three penalties for Harlequins, who had led 9-3 after 30 minutes. Harlequins finished the half without their captain Will Skinner, who was given a yellow card for handling in the ruck.
Tigers hooker Benjamin Kayser was also sent to the sin bin for the same offence earlier in the half.
Head coach Heyneke Meyer recalled England internationals Martin Corry, Jordan Crane, Tom Croft and Dan Hipkiss to the Tigers team, while Benjamin Kayser came into the front row and Scott Hamilton moved to full-back in the absence of the injured Geordan Murphy. Harlequins made a late change to their starting line-up with De Wet Barry replacing Gonzalo Tiesi at centre.