Gregory Nasmyth's gift pushed Lib Dem donations to £1,972,904, compared with £1,970,055 for the Labour Party.
It is the first time since donations records began in 2001 that Lib Dem quarterly donations have beaten Labour.
Both were dwarfed by the £3,610,983 donated to the Conservatives. Labour accused its rivals of increasingly relying on "a small pool of donors".
Other donation totals reported over the same period include £46,228 for the Greens, £39,750 for the Co-operative Party, £3,228 for UKIP and £30,000 for the Women's Equality Party.
Mr Nasmyth, who last month gave Greenpeace £500,000, has been upping his donations since the sale of his family's oil data company, Argus Media.
On his website he says he supports "environmental and progressive causes". It is thought that his large donation to the Lib Dems is the first he has made as an individual to a political party.
His £1m was donated during a period when the Lib Dems caused a major upset in the Richmond Park by-election, overturning a 23,015 Conservative majority after the sitting MP Zac Goldsmith resigned in protest at the government's backing for a third Heathrow runway, before unsuccessfully running as an independent.
Liberal Democrat president Baroness Brinton accused Labour of being "Theresa May's cheerleaders for a hard Brexit" and said her pro-EU party was "providing the real opposition to the Conservative Brexit government".
The Conservatives' largest single donations were £266,000 from mining millionaire Michael Davis and £233,000 from property developer David Rowland.
Labour's largest donors during the quarter were unions - Unite gave Labour £440,622, Usdaw donated £368,693 and the GMB £332,808.
A spokesman for the Labour Party said: "Labour is a mass membership party, proud to be funded by members and working people.... while our main rivals increasingly rely on a small pool of donors."
The Electoral Commission published the latest figures on its website which also showed reported donations for 2016 totalled £41,174, 873 - down on the previous, general election, year when £67,119,770 was donated.
A £1m donation meant the Lib Dems reported more funds raised than Labour in the last quarter of 2016.