Kiprop pulled ahead of the field shortly before the bell and raced away to win in three minutes 27.72 seconds to make him the fourth fastest man of all time over the distance.
Britain's Olympic 5,000 and 10,000 metres champion Farah said before the event that he was dropping down to the shorter distance to work on his speed and the move paid off as he was dragged round in a European record of 3:28.81.
"I'm definitely pleased, training has been going pretty well," the 30-year-old, who goes sixth on the all-time list, told the BBC.
"The aim was to come out here and work on my speed. It would have been nice to get closer to Asbel but he's got another gear and he kept stretching away," added Farah who plans to move up to the marathon next year.
Controversial sprinter Justin Gatlin won the men's 100 metres, which was run against the backdrop of last weekend's revelations that leading sprinters Tyson Gay and Asafa Powell had failed dope tests.
American Gatlin, who served a four-year doping ban from 2006, got a great start and won in 9.94 seconds, in a race missing world-record holder Usain Bolt, to show he is likely to be the Jamaican's main contender in Moscow.
Murielle Ahoure of the Ivory Coast put herself in the mix for the world 200 title after blasting out of the blocks and holding off American Tiffany Townsend and Olympic 100 metres champion Shelly-Ann Fraser-Pryce for victory in a national record of 22.24.
Farah would have watched the 5,000 metres, for which he is world champion, with interest as Kenyan Edwin Soi ran the fastest time of the year, 12:51.34, to beat the Briton's meeting record set in 2011. Former Kenyan Albert Rop, now competing for Bahrain, was second in an arena record of 12:51.96.
Time is running out for world and Olympic 100 hurdles champion Sally Pearson, who is still a way off her best after returning from a hamstring injury last month.
The Australian faded badly over the last three hurdles to finish fifth behind American Queen Harrison who won in 12.64.
Olympic silver medallist Brigetta Barrett treated the crowd to a dance routine after clearing 2.01 first time in the high jump which was enough for victory.
Renaud Lavillenie of France dominated the pole vault competition, securing victory with a Diamond League record and world-leading 5.96 metres, 18 centimetres higher than American Brad Walker in second.
(Writing by Alison Wildey in London; Editing by Clare Fallon)
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