A 2011 mass shooting left Gabrielle Giffords, then a Democratic congresswoman, partly paralyzed and unable to speak fluently. She has since built a powerful advocacy group.
Senator Catherine Cortez Masto defeated Adam Laxalt, the state’s former attorney general. Democrats now will try to add to their control of the chamber in Georgia’s runoff election on Dec. 6.
In Arizona and Nevada, Republicans’ path to victory appeared to narrow, though both races remain close. The G.O.P.’s odds of success are greater in the House.
Senator Mark Kelly, a Democrat, holds an edge in his bid for re-election, but the race for governor appears to be a true tossup, even as several Republican candidates sow doubts about the results.