Gonzaga’s opportunity to rise to No. 1 began Tuesday when No. 1 Villanova, No. 2 Kansas and No. 4 Kentucky lost within a few hours of one another. Two days later at home, the Bulldogs dismantled San Diego, a .500 team, by 79-43, and then, on Saturday, they romped over Pepperdine, the W.C.C.’s last-place team, 96-49, in Malibu, Calif. By then, the No. 3 Bulldogs already had become the presumptive No. 1.

That would put this year’s team at least on par with the ones that are remembered in banners hanging above their heads every time they take the floor at Spokane’s McCarthey Athletic Center. The earliest banner memorializes an N.C.A.A. tournament berth in 1995. Other banners recognize a stunning run to the round of 8 in 1999, and trips to the round of 16 in the two seasons after that — 18 qualifications in a row through last year.

There were hints during Gonzaga’s rout of San Diego that these Zags could differ from the past squads that fell short of the Final Four.

Williams-Goss scored at will, piling up 25 points, and the lanky junior forward Johnathan Williams slashed his way to a double-double.

The senior Przemek Karnowski, a 7-foot-1, 300-pound center from Poland, leads the conference in field-goal percentage, but it is his court vision that really impresses, his ability to spot cutting teammates and hit them in stride.