Kemi Badenoch says the Scottish Conservatives' first by-election win since 1973 sends a message to Labour and the SNP.
The Aberdeen South seat, vacated by the SNP's Stephen Flynn, was won by Tory MSP Douglas Lumsden.
Shortly afterwards the SNP claimed a victory in the Arbroath and Broughty Ferry by-election where Lara Bird held the seat for the party.
Lumsden, who is unable to sit in both parliaments due to a Holyrood ban on so-called dual mandates, is to resign from Holyrood just six weeks after winning re-election as a north-east MSP.
Badenoch told jubilant party activists: " I cannot tell you how thrilled I am to be able to welcome Douglas Lumsden to parliament."
The Conservative leader, who was flanked on stage by Lumsden and Scottish Tory leader Russell Findlay, thanked voters for putting their trust in the party.
She also praised the positivity of Lumsden's campaign and said the result had national significance.
Badenoch said the media had focused on the Makerfield by-election where Manchester Mayor Andy Burnham won 55% of the vote.
He is now expected to challenge Sir Keir Starmer's leadership.
Badenoch said: "The Makerfield by-election was about one man's job.
"The Aberdeen South by-election was about thousands of jobs all over the country but especially in the oil and gas sector."
She added: "Aberdeen has sent a message to the Labour government and the SNP that we will not be ignored.
"Aberdeen will not be ignored. The sector will not be ignored."
Badenoch also said the country needed to think about national security and energy security more than ever.
Scottish Conservative leader Russell Findlay described the result as a "sensational victory".
He added: "This was a referendum on oil and gas."
The Scottish by-elections were triggered when sitting MPs - Flynn and his SNP colleague Stephen Gethins - resigned from the House of Commons after being elected to Holyrood.
First Minister John Swinney said he understood why the SNP lost.
"The Conservatives mobilised a campaign which was about capturing the understandable anger there is in Aberdeen and the northeast about the issues affecting the oil and gas sector," he said.
Swinney said he was trying to help the industry by urging Labour to scrap the Energy Profits Levy.
At present, it means that operators are handing over 78% of their profits to the Treasury.
Aberdeen is at the heart of the debate around the UK's energy future, and the UK government has chosen the city as the home of GB Energy - its fledgling publicly-owned energy company.
Lumsden, a former oil and gas worker, said his constituents had sent a message that "the destruction of the oil and gas industry must stop now".
The north-east MSP defeated SNP candidate Richard Thomson, a former MP for Gordon, by a margin of more than 6,000 votes, with the Tories taking almost half of all ballots cast.
Amy Cameron, from Greenpeace UK, said "false promises" from the Tories would not deliver a prosperous economic future for people in Aberdeen.
She said a just transition has to be strong enough for people to "let go of the industry that built their community" and "trust that the new economy will be ready to catch them".
In Arbroath and Broughty Ferry, Lara Bird won the seat on Scotland's east coast for the SNP with a majority of more than 5,000 votes over the Conservatives.
Bird, from near Kirriemuir, is a qualified lawyer who has worked as an SNP researcher and adviser at Westminster.
She said voters had "rejected the politics of division and hate" and made it clear that Scotland's future "lies with independence".
Labour slipped from second to fourth in the constituency, with Reform in third.
Flynn, who is now Scotland's economy secretary, responded to the loss of his old seat on social media, posting: "A tough night in Aberdeen that some will need to reflect on, quite heavily."
He added: "We lost Aberdeen South to the Tories in 2017, and we won it back two years later.
"I've no doubt that we can do so again. If we get things right."
Lumsden will have 49 days to resign as an MSP, under Holyrood's dual mandate ban.
His place in the Scottish Parliament will be taken by the next candidate on the Conservatives' North East Scotland list, Fraserburgh councillor James Adams.
The Conservatives last won a Westminster by-election north of the border in 1973, when they held Edinburgh North.
The Scottish Tories had not gained a seat in a Westminster by-election since 1967, when they took Glasgow Pollok from Labour.
The Aberdeen South defeat comes just six weeks after the SNP won a comfortable victory in the Scottish election.
Within weeks the party was rocked by a scandal surrounding former chief executive Peter Murrell, who admitted in court to embezzling more than £400,000 of SNP funds over a 12-year period.
He is due to be sentenced next week.
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