In Alaska, Democrat Mary Peltola and incumbent Republican Senator Dan S Sullivan advanced in the state's unusual non-partisan primary.
Democrats see the contest among their best opportunities to pick up the one of four seats they need to win control of the 100-seat chamber in November's midterm election.
In Florida, left-wing state lawmaker Nixon scored a surprise victory as she defeated former national security official Alex Vindman, who rose to prominence in 2019 when he testified to Congress during Republican President Donald Trump's first impeachment.
Vindman raised 16 times as much money as Nixon.
Nixon, 42, has been active in Florida's labour movement and was reprimanded for disrupting a Florida House vote when she protested congressional redistricting legislation with a pink megaphone.
In her campaign, she urged voters to "make sure you wear your pink to the polls".
She will face Republican senator Ashley Moody in November's general election.
Analysts say Moody is favoured to win the match-up and finish the remaining two years in the term of former Florida senator Marco Rubio, who now serves as Trump's secretary of state.
Republicans are also favoured to win the race to replace term-limited Governor Ron DeSantis, in which Republican Byron Donalds will face Republican-turned-Democrat David Jolly.
In Alaska, Democrat Peltola, a moderate who formerly held the state's sole House seat, will face incumbent Republican senator Dan S Sullivan after the state's non-partisan primary on Tuesday.
Alaska has not had a Democratic senator since 2014, but the race is seen as competitive.
In Florida, two veteran Democratic lawmakers cleared their first hurdle as they sought to survive a Republican redistricting that forced them to run in new seats.
Representative Jared Moskowitz fended off challenger Oliver Larkin, who was backed by the Democratic Socialists of America, in Florida's 25th district, and will face Republican Scott Singer in one of the few congressional races in the state seen as competitive.
Representative Debbie Wasserman Schultz, first elected to Congress in 2004, won her party's nomination to represent a district centred in Broward County.
Florida's new map could leave the state with a House delegation of 24 Republicans and only four Democrats.
States usually redraw their congressional maps only at the beginning of every decade, to reflect census results.
But several have redistricted in the past year at Trump's urging to shore up the Republican majority in Congress, prompting some Democratic-led states to redraw their own maps in response.
Republican representative Cory Mills, who is embroiled in ethics investigations, was defeated in his central Florida primary for re-election by former broadcast news anchor Ryan Elijah.
Mills has denied allegations of campaign finance law violations and sexual misconduct now being probed by the House ethics committee.
