Returning from an operation in late January, the 503rd-ranked Murray triumphed in full sets 7-6 (6), 6-7 (4), 6-1 in two hours and 52 minutes, earning his second straight victory for the first time at the tour level after his comeback, reports Xinhua news agency.
"If you watched the end of the second set and pretty much the whole of the third set, I tried to keep the points short. I started coming to the net a lot more. I did the right thing and started to shorten the points, kind of didn't make it a physical battle," commented Murray.
After both players maintained serves early on, Murray went ahead by registering a break, but his fellow Briton soon responded and went on to force a tie-break, where Murray converted his fourth set point.
A forehand winner guided Norrie to a 4-2 lead in the second set. It was the 2016 champion that turned around and put the match into another tie-break before Norrie had the last smile on his third set point.
Murray stormed to a 5-0 advantage in the decider, and never looked back by serving for the win. Murray will next take on the winner between top seed Dominic Thiem and Chinese wild card Zhang Zhizhen.
( With inputs from IANS )