Paul Biedermann of Germany was fastest in 1 minute, 45.30 seconds.
Swimming his first individual event, Phelps clocked 1:45.60. Danila Izotov of Russia qualified third for the semifinals later Monday.
Phelps set the world record of 1:42.96 at last year's Beijing Olympics.
On Sunday, Biedermann broke Ian Thorpe's seven-year-old world record in the 400 free.
Phelps also won his first gold Sunday, swimming the leadoff leg for the Americans in the 400 free relay.
© 2009 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.
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Bruce Maxwell of the Oakland Athletics has become the first major league baseball player to kneel during the national anthem.
The Golden State Warriors say they will not go to the White House when they visit Washington early next year, announcing the decision hours after President Donald Trump tweeted he was withdrawing the invitation.
The National Football League and its players' union on Saturday angrily denounced President Donald Trump for suggesting that owners fire players who kneel during the national anthem.
The Los Angeles Dodgers clinched their fifth straight NL West title, beating the San Francisco Giants 4-2 on Friday night as Cody Bellinger set an NL rookie record with his 39th home run.