Senior Niels Giffey later hit a three-pointer in the corner for his first points since the game's opening moments, and when the Huskies (29-8) made their free throws in the final minute, the UConn fans packing Madison Square Garden could celebrate.
Dustin Hogue scored a career-high 34 points for third-seeded Iowa State (28-8), but Big 12 player of the year Melvin Ejim was three-of-13 shooting for seven points.
UConn will face fourth-seeded Michigan State on Sunday for a trip to the Final Four. The Spartans knocked off No. 1-seeded Virginia, 61-59, in the other semifinal.
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.
Iowa State's Naz Long missed a three-pointer with UConn clinging to a 70-65 lead and less than a minute left, and 6-1 Shabazz Napier pulled down the rebound and was fouled by Hogue. The senior calmly drilled both free throws.
Napier, the American Athletic Conference player of the year, drained four early three-pointers, then made only one more field goal the rest of the way. But the quick start by Napier and backcourt mate Ryan Boatright opened up space for the 6-foot-9 Daniels, an inconsistent junior who can score all over the court when he's on.
Since a stretch in late February and early March when he failed to reach double figures in four consecutive games, Daniels had averaged 15 in his last six outings before Friday. He shot 10 of 15 and pulled down 10 rebounds against Iowa State.
After Napier's difficult early three-pointers -- he was falling away on two of them and stepping back to open a sliver of space on a third -- Boatright and Daniels took over. The three combined for all but six of the Huskies' points as they built a 36-26 halftime lead.
UConn is back in the NCAA tournament after academic sanctions kept the Huskies out last season. They were also ineligible for their last Big East tournament at the Garden as a member of the conference, but looked right at home Friday.
The last time UConn made it this far, the Huskies won a national title when Napier and Giffey were freshmen.