Daniels was 10 of 15 from the field.
"With our seniors on this team, I just want them to go out with a bang," he said.
Dustin Hogue scored a career-high 34 points for Iowa State, but Big 12 player of the year Melvin Ejim was 3 of 13 for seven points, more than 11 below his average.
The Cyclones, in the Sweet Sixteen for the first time since 2000, were playing their second game without third-leading scorer Georges Niang, who broke his foot in their tournament opener.
They trailed by 16 points with less than 7½ minutes to go, but nearly came all the way back behind Hogue's inside scoring.
"That's who these guys are, they're fighters," coach Fred Hoiberg said.
These were the first NCAA tournament games played at Madison Square Garden since 1961 and there was a sellout crowd of 19,314 on hand.
There may be a few more squeezed in on Sunday.
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