Farah won 5,000 metres gold to add to his 10,000m title in Zurich, while Rutherford added the European long-jump title to his Olympic and Commonwealth golds.
There was also unprecedented success for Britain in the relays, with the men winning both 4x100 and 4x400 titles, and the women stunning favourites France to claim 4x100 gold, setting a British record of 42.24 seconds.
Farah has had a difficult season, with his ill-fated attempt at the London Marathon followed by an illness which ruled him out of the Commonwealth Games.
But, safe in the knowledge he is the fastest finisher in distance running, Farah stayed at the front of a slow tactical race before searing away from Azerbaijan's Hayle Ibrahimov.
"There have been some down times this year but I've got over it," Farah told BBC Sport.
"Training has gone well in the last couple of weeks and that gave me confidence. History is important to me and it feels great to make my country proud."
It is Farah's fifth European championship gold, and he is now reigning double European, World and Olympic champion.
His British team-mate Andy Vernon took bronze to add to his silver medal in the 10,000m.
Final medal table of the European Athletics Championships (http://www.european-athletics.org/)
Earlier in the day Great Britain's claimed 4x400m gold. Conrad Williams, Matt Hudson-Smith, Michael Bingham and Martyn Rooney powered to victory in two minutes 58:80 ahead of Russia and Poland.
Britain soon topped the table in Zurich and were also ensured of a best ever European Championships as 200m champion Adam Gemili anchored his 4x100 team to claim yet another gold, pulling away from Germany's Lucas Jakubczyk with 60m or so remaining.
Meanwhile, Rutherford was busy proving that his Olympic exploits were no fluke by dominating the long jump, his best effort of 8.29 a full 14cm ahead of Louis Tsatsoumas in silver. Indeed, the Milton Keynes star's second best jump of 8.27 would have won easily.
"It is a real sense of relief because I was seeing how well the British team was doing and everybody was saying to me, 'You have to go out and do it.' I was so pleased I could."
And the Brits were not finished, as the women ran a brilliant relay to destroy the highly-fancied French in the 4x100. GB had taken bronze in the women's 4x400 earlier.
Greg Rutherford in action at the European Athletics Championships (AFP)
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