Willis, coming off a sizzling victory in Boston last week, came up on the right shoulder of Centrowitz with 100 meters left but failed to get past the American, who won in a year's best three minutes 51.35 seconds, 11 hundredths of a second ahead of the Kiwi.
Pat Casey was third in 3:54.36 ahead of eight-times Wanamaker winner Bernard Lagat, whose 3:54.91 set an over-40 masters record by more than three seconds over the 1994 mark set by Ireland's Eamonn Coghlin.
Ten runners clocked under 3:58 on the fast Armory track as several world-leading times were posted.
Sally Kipyego of Kenya won the 3,000 meters in a 2015 best of 8:41.71, and Murielle Ahoure of the Ivory Coast clocked a year's fastest 7:05 to win the women's 60 meters.
Brycen Spratling ran the fastest indoor time ever in the rarely run 500 meters, timing 1:00.06 to beat the 1987 mark of 1:00.17 by Ken Lowery.
The racing highlight came in the meet-ending men's mile.
Centrowitz, the world championships 1,500 meters silver medallist, was well in front before Willis surged on the last lap.
"Doing the last three laps by myself that's not ideal for me to run 3:49," he said about his goal of a U.S. record.
"Once Willis came up on me in the back stretch I knew if I let him by me that it was game over...I went all-out just to fight him to the corner."
Willis's time of 3:51.46 lowered the national record he set last week.
"I've learned that whoever leads with a hundred to go in indoor track normally will win it, so I gave everything I could to pass him there but I couldn't," said Willis, the 2008 Olympic 1,500 meters silver medallist.
Women's miler Shannon Rowbury looked like threatening the U.S. record as she opened a big lead before slowing before the finish to win in 4:24.32.
"Just me getting tired, nothing wrong, nothing hurt," she said. "I just had that elephant on my back the last 50 meters."
Also hitting the wall near the finish was Olympic 400 meters champion Sanya Richards Ross, who grabbed the lead with 100m to go but slowed before the tape to finish second behind Francis Phyllis's 53.14.
(Editing by Patrick Johnston)
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