The Scotsman, who has never reached further than the final eight in this competition, struggled in the early stages of the first set as Janowicz pushed his opponent with strong returns and precise forehands to make Murray work around the court.
Murray eventually secured a break of serve and while his Polish competitor continued to push the Brit, Murray was able to hold and clinch the opening set.
The second set was forced into a tie-break after Murray was unable to build on his lead and Janowicz came out victorious by executing tricky shots, which the Scotsman was unable to respond to.
Murray stumbled in the third and final set by losing a break of serve immediately, which Janowicz capitalised on. While the Scot tried to delay the Pole's victory, Janowicz was able to convert his match point and grab a spot in the quarter-finals.