Penguins defenseman Kris Letang hooked McDavid on a breakaway chance late in the second period, awarding the Hart Memorial Trophy winner with a penalty shot.
McDavid took the puck at center ice and glided in slowly before dangling in front of Murray. The Penguins' goaltender traced the puck and made an acrobatic glove save to deny a quick wrister from McDavid.
Murray's save preserved Pittsburgh's 2-1 lead entering the third period. He had 38 saves and a .974 save percentage against the Oilers as the Penguins cruised to a 3-1 victory and season sweep of Edmonton at PPG Paints Arena in Pittsburgh.
Bryan Rust, Teddy Blueger and Jared McCann each scored for the Penguins.
Pittsburgh captain Sidney Crosby finished with one assist in his head-to-head matchup against McDavid. McDavid tallied an assist on Leon Draisaitl's goal in the first period, but otherwise had a quiet night against Murray.
Murray has a 17-9-1 record in 28 starts this season with a 2.82 goals-against average and .916 save percentage. He has three shutouts.
McDavid has recorded 82 points (31 goals, 51 assists) in 55 games this year.