Conservatives hold Sleaford as Labour pushed into fourth
Conservative Caroline Johnson has won the Sleaford and North Hykeham by-election, while Labour were pushed into fourth behind UKIP and the Lib Dems.
The Conservatives held the seat, after former MP Stephen Phillips quit, citing "irreconcilable policy differences" with the government.
Dr Johnson won 17,570 votes to beat UKIP's Victoria Ayling, who had 4,426.
Labour slipped from second place in 2015 to fourth - described by one veteran Labour MP as "humiliating".
Consultant paediatrician Dr Johnson said her election would boost Theresa May's support on Brexit.
She said: "I look forward to strengthening the government's majority in Parliament so Theresa May, our prime minister, can get on with the job of triggering Article 50, leaving the European Union and building a country and economy that works for everyone."
The result in full:
Caroline Johnson: (Conservatives) - 17,570
Victoria Ayling: (UKIP) - 4,426
Ross Pepper: (Liberal Democrats) - 3,606
Jim Clarke: (Labour) - 3,363
Marianne Overton: (Lincolnshire Independent) - 2,892
Sarah Stock: (Independent) - 462
The Iconic Arty-Pole: (Monster Raving Loony Party) - 200
Paul Coyne: (Independent) - 186
Mark Suffield: (Independent) - 74
David Bishop: (Bus Pass Elvis Party) - 55
The seat has returned Conservative MPs since it was formed in 1997 and Mr Phillips, who resigned in November, had a majority of more than 24,000 votes in 2015.
Although he backed leaving the EU, he had since been critical of the government's approach to Brexit.
Dr Johnson won with a 13,144 majority after securing 53.51% of the votes, while UKIP came in second with 13.48%.
Liberal Democrat candidate Ross Pepper won 3,606 votes to clinch third, narrowly ahead of Labour's Jim Clarke who was fourth with 3,363 votes.
Analysis by Tom Bateman, BBC political correspondent
There were few words from the victor in Sleaford and North Hykeham.
Dr Caroline Johnson was whisked out of the hall without a word to reporters, after a short speech in which she looked forward to helping the prime minister "get on with the job" of leaving the EU.
It was not the first time a brand new Conservative MP had left a by-election in a hurry.
With the party's message on Brexit being closely managed, it may have been a conscious choice to let more senior MPs do the talking.
And it is likely there will be quiet comfort for Theresa May at this result.
In June, voters in this rural Lincolnshire seat decisively backed Brexit - the verdict here would be keenly watched for any messages about the government's EU withdrawal strategy so far.
There were rumblings during the by-election campaign from UKIP that voters may want to send a message to Mrs May for, in their view, "backsliding on Brexit".
But it didn't happen.
UKIP came a distant second - a result their new leader Paul Nuttall celebrated as a "small step on a long road", despite the party's vote share falling compared with last year's general election.
But the most acute soul searching may be for Labour, beaten into fourth place by the Liberal Democrats.
BBC political editor for Yorkshire and Lincolnshire Tim Iredale, who filmed Dr Johnson after the result, tweeted that she had been "rushed away from count after refusing to speak to the media".
The Lincolnshire seat is in an area which voted heavily to leave the EU.
UKIP's former leader Nigel Farage and his successor Paul Nuttall had been on the campaign trail, supporting Ms Ayling - a former Conservative who stood for the Tories in Great Grimsby in 2010.
Ms Ayling said coming in second was a "great result" for UKIP as it showed "more people are trusting us to deliver".
Mr Nuttall said the result was a "really good way to get my leadership off the ground".
He added: "If someone would have offered me second place at the beginning of the campaign, considering we were in the middle of a leadership election and the party resembled a bit of a shambles over the summer, I would have bitten their hand off."
Liberal Democrat leader Tim Farron said his party's "strong result" showed they were "back as an electoral force" in areas that had voted to leave, as well as remain, in the EU.
He went on: "With Labour yet again nowhere, and after losing their deposit in Richmond, the Liberal Democrats are the real opposition to the Conservative Brexit government."
Labour MP Jess Phillips said the party's stance on Brexit was confusing and it was hard for leader Jeremy Corbyn, given his political background, to address voters' concerns on immigration in areas like Lincolnshire.
"When people are putting a cross in a box, clarity is everything," she told BBC Radio 4's Today. "Labour needs to have a very clear position and for everybody to be saying the same thing and at the moment that is not the case."
And David Winnick, the veteran Labour MP for Walsall North, said: "If we were to continue in this way then the indications are 2020 will be an electoral disaster."
He also told BBC 2's Daily Politics: "To be beaten into fourth place by the Liberal Democrats was humiliating ... My fear is that we're not in touch with ordinary people anywhere, to the extent that it's necessary to make a real impact in the country."
Former Conservative Chancellor George Osborne said Labour's showing was evidence of its "disintegration", tweeting that this was "not good for democracy".
The turnout for the by-election was 37.1% according to North Kesteven District Council, down from 70.2% at the general election last year.
Following their victory, the Conservatives have a majority of 10 in the House of Commons but, given that the four Sinn Fein MPs do not take their seats, their working majority is effectively 14.