Murray beat Wawrinka in the Cincinnati Open to set up a meeting with Norrie.
The 35-year-old Murray defeated the older man in the first round.
Murray is hoping to get a seeding at the US Open, which starts on 29 August.
The British number one won a hard fought match against the Danes.
Both of them fought back from injuries in recent seasons to show their love for the sport.
It was fitting that their fight and determination was visible again in a three hour battle in Cincinnati.
Three break points were not taken by Wawrinka in the first set, and that hold proved crucial as Murray played superbly in the tie-break to lead.
Wawrinka only returned to the tour in April after 13 months out with a foot injury and needed treatment on the same leg, as he was leading 2-1 in the second set.
He broke for 6-3 to serve the set.
Murray put the set back on serve without putting too much pressure on Wawrinka.
Murray was broken for the second time in the set at 5-5 as Wawrinka fought back to force a decider.
After being broken in the second game, Murray broke straight back and was treated by himself at the changeover.
The set continued on serve until Murray broke for a 4-3 lead with a rasping return and then served out to win the match.
A tense game saw Murray unable to take any of three match points - including after being docked a first serve on the third for a second time violation - before taking the fourth with a huge serve down the middle.
Murray said that his body was feeling the best it had in a long time, but that his game had room for improvement.
He said that he would like his tennis to be better at times.
It has been difficult to stay fit and healthy in the last few years.
I want to get into more tournaments and not have to rely on wild cards.
Murray said he was different to how Stan plays being a lefty.
He hits on the backhand with a heavy top spin. There won't be many surprises for me because we have been on the court together.
Norrie earned the first main-draw victory of his career at Cincinnati with a patient win over a talented teenager.
Murray said that he was different to how Stan played, being a lefty.
The backhand was flat and the forehand was heavy. There won't be many surprises for me because we have been on the court together.
Norrie, ranked 11th in the world, lost serve for the first time in his career at 4-2 in the opening set but immediately broke back to take the lead.
Norrie won the tie-break when Rune ended the rally with a long hit.
After hitting two balls out of the stadium and hitting the net with his racquet, the Danes was frustrated and went for a toilet break.
The moment of reflection helped as he broke in the first game of the second set and, after the pair exchanged breaks in consecutive games for 4-4 and 4-5, he made sure the match would be decided by a decider.
There were two breaks of serve in a row midway through the set before Norrie was able to get the win.
All Rights Reserved © 2024
