Yuh-Line Niou won a six-way race on Tuesday for the Democratic nomination to inherit the State Assembly seat once held by Sheldon Silver, in a repudiation of the stubborn grip Mr. Silver held on his Lower Manhattan district for four decades — held, that is, until his conviction late last year on federal corruption charges.

Yet Mr. Silver, the longtime former speaker who is appealing his conviction, still had enough influence in the district during the special election for the seat in April to help install an ally, Alice Cancel, in his place. Ms. Niou’s victory over Ms. Cancel, as well as four other opponents who promised a post-Silver fresh start for the district, may confirm that Mr. Silver’s clout is truly on the wane — and that voting patterns are beginning to reflect shifting demographics in the area, which is nearly half Asian.

In another closely watched primary race in a district encompassing neighborhoods in demographic flux in northern and western Manhattan, Marisol Alcantara, a Dominican labor organizer, prevailed in a four-way contest for the Democratic nomination to replace State Senator Adriano D. Espaillat, who is running for Congress, in Senate District 31. Mr. Espaillat had personally campaigned for Ms. Alcantara as well as another candidate of Dominican descent, Carmen De La Rosa, who was trouncing an incumbent assemblyman, Guillermo Linares, in his Inwood district, 46 percent to 32 percent.

As Dominican voters in Upper Manhattan made their numbers felt, Mr. Espaillat’s status as a local power broker seemed on the rise: His two candidates even held their victory party together.