Murray, the world number two who was eliminated a week ago in the Montreal third round, made sure the mistake was not repeated as he needed just 70 minutes to see off his Russian opponent and move into a match with Julien Benneteau of France.
Murray immediately took a double break of Youzhny, whom he has now beaten in all four of their matches, including the Wimbledon third round on the way to his historic title last month. Murray took the opening set in 33 minutes.
The Scot lost his only service game midway through the second set but did not show alarm with the comfort of another break in hand. Murray took victory on a Youzhny forehand error.
"I put a lot of pressure on myself to get through this one," said the winner. "With the US Open only a couple of weeks away, I need to stay in form."
Murray has twice won the Midwest event, both times at the expense of Novak Djokovic, in 2008 and 2011.
Elsewhere, German 11th seed Tommy Haas defeated Spain's Marcel Granollers 6-4, 6-1 while Belgian qualifier David Goffin surprised Montreal semi-finalist Vasek Pospisil of Canada 7-5, 1-6, 7-6 (8/6) after saving four match points.
In women's play, seeded Italians Sara Errani and Roberta Vinci both advanced.
Number six Errani defeated Polona Hercog 6-4, 5-7, 6-4 while Vinci won a struggle with German Andrea Petkovic 6-4, 6-7 (3/7), 6-3.
Top seed Djokovic and Rafael Nadal were opening their campaigns later at the last major tune-up prior to the start of the US Open a week from Monday.
Australian Samantha Stosur, seeded 11th, continued her progress, beating Jamie Hampton 6-3, 7-6 (7/3).
Results from the ATP and WTA Western and Southern Open (x denotes seed):
Andy Murray (GBR x2) bt Mikhail Youzhny (RUS) 6-2, 6-3
Tommy Haas (GER x11) bt Marcel Granollers (ESP) 6-4, 6-1
David Goffin (BEL) bt Vasek Pospisil (CAN) 7-5, 1-6, 7-6 (8/6)
Juan Martin Del Potro (ARG x7) bt Nikolay Davydenko (RUS) 7-5, 7-5
Feliciano Lopez (ESP) bt Jrmy Chardy (FRA) 6-4, 2-2 ret
John Isner (USA) bt Richard Gasquet (FRA x8) 7-6 (8/6), 6-2
Samantha Stosur (AUS x11) bt Jamie Hampton (USA) 6-3, 7-6 (7/3)
Sara Errani (ITA x6) bt Polona Hercog (SLO) 6-4, 5-7, 6-4
Roberta Vinci (ITA x12) bt Andrea Petkovic (GER) 6-4, 6-7 (3/7), 6-3
Serena Williams (USA x1) bt Eugenie Bouchard (CAN) 4-6, 6-2, 6-2