ALBANY — In the moments after Connecticut advanced to the Final Four on Sunday for the 12th year in a row, blue, yellow and orange confetti rode the waves of Coach Geno Auriemma’s undulating hair. The pieces dusted the shoulders of his blue suit jacket and hid inside the top of his unbuttoned shirt.

For Auriemma, the caretaker of the most dominant women’s basketball program in history, this could get old. In some years, it has. In those years, the 65-year-old Auriemma would like to point out, people seemed to forget how hard it can be to march through an N.C.A.A. tournament. UConn’s invincibility was perceived to be as simple as an uncontested layup. Perfection was expected.

This is not one of those years, at least by UConn’s preposterously high standards. For Auriemma, then, the celebration that followed Sunday’s 80-73 victory over No. 1-seeded Louisville in the Albany Region final — the confetti, the long embraces, the snips of the net — brought about a joy that even his usual sarcasm could not suppress.

With wins by Oregon and Connecticut on Sunday, half of the women’s Final Four field is set. The Ducks will face the winner of Monday’s game between Baylor and Iowa, while the Huskies will meet the winner of the game between Notre Dame and Stanford.