Complex sentence: She was one of eight women who ran for the legislature that year, but was the only one to win her race, a feat made more impressive because she unseated a long-time incumbent, John E. Davis of Mesquite.
Split into simpler sentences: She was one of eight women who ran for the legislature that year, but was the only one to win her race. She gained attention by unseating a long-time male incumbent, John E. Davis of Mesquite.