The result is a rebuke of Ms Lake, who has peddled the false claim that Donald Trump won the 2020 US election.
In her victory statement, Ms Hobbs said that in this moment of division she would work for everyone in the state.
Ms Lake appeared to suggest that the result was incorrect, and that some votes for her had not been counted.
Republicans must win at least 218 seats to claim a majority in the House of Representatives, a prospect that has sharply narrowed.
In a midterm election that has further highlighted the stark partisan divisions in America, Ms Hobbs called for unity, saying she would work for those Arizonans who did not vote for her.
“Even in this moment of division, I believe there is so much more that connects us, she said.
Her opponent, Ms Lake – who was endorsed by Mr Trump told the BBC during campaigning that the former president should not need to run again in the 2024 election because he won the last election. She predicted he would come back with a vengeance. There is no evidence that the 2020 election was stolen.
Ms Lake’s defeat sees her join the ranks of pre-eminent Trump-backed election deniers who lost last week. But a BBC News tally of results found at least 125 election deniers have won races for the House, Senate and governorships.
The midterm elections are also for Congress, including all seats in the House of Representatives and one third of those in the Senat
The Biden administration had feared that a loss of power in Congress would bring the president’s agenda to a halt. However, the Democrats have retained control of the Senate, and the House has not yet been called.
If the two parties split control of Washington, Democrats will maintain our positions, but voters should not expect much of anything President Biden said on Monday.
Speaking to reporters in Indonesia, where he is attending the G20 summit, Mr Biden said the results had sent a very strong message around the world that the United States is ready to play and wants to remain fully engaged in the world.
He noted there was a strong rejection of election denialism political violence and voter intimidation. But he warned that without a majority in the House, Democrats would be unable to codify abortion rights through legislation, a key priority for liberal voters.
Out of the 11 House races that still remain to be called, most are in western and southwestern states, including California and Arizona.
Newly elected members of Congress, including the first lawmaker from Generation Z and the first openly gay Republican, have already begun arriving in Washington for orientation.
History suggests the party controlling the White House usually loses seats in a midterm election, and Democrats’ performance this year is considered the best for a sitting party in at least 20 years.
That has endangered leadership bids for the top Republicans in the Senate and House ahead of the party’s internal elections on Tuesday.
House Minority Leader Kevin McCarthy – who hopes to succeed Nancy Pelosi as Speaker in the next Congress and Senate Minority Leader Mitch McConnell are both reportedly scrambling to garner support from their colleagues.
Divisions within the party have been on full display in recent days as former President Donald Trump, who has received some of the blame for a poor showing, prepares to launch another presidential run later this week.
Mo Brooks, a Republican representative in Alabama and once a strong supporter of Mr Trump, said it would be a bad mistake for the party if the former president was their nominee in 2024.
Donald Trump has proven himself to be dishonest, disloyal, incompetent, crude and a lot of other things that alienate so many independents and Republicans. Even a candidate who campaigns from his basement can beat him, Mr Brooks told AL.com.