Farah clocked 13 minutes 11.77 seconds, ahead of Kejelcha (13:12.59) and Kenyan Edwin Cheruiyot Soi (13:17.17).
"This victory is a way to answer some of the critics regarding my coach," he told www.lausanne.diamondleague.com.
"I had a great finish, overall I am happy with the way the race went. It was my first time in Lausanne and I really enjoyed starting my season here."
Last month Salazar and Farah's training partner and U.S. Olympic silver medalist Galen Rupp were accused of violating anti-doping rules in a BBC documentary. Both men have denied any wrongdoing.
No allegations were made against Farah and he has reiterated his innocence on a number of occasions. He pulled out of last month's Diamond League meeting in Birmingham, citing stress.
The 32-year-old is due to run in the 1,500 metres in Monaco on July 17 and the 3,000 metres in the Anniversary Games at London's Olympic Stadium the following week before he bids to defend his world 5,000 and 10,000 titles in China next month.
American Justin Gatlin, the fastest man in the world this year, underlined his dominance as he cantered to victory in the 100 metres ahead of Asafa Powell and Tyson Gay.
Gatlin, 33, streaked out of the blocks and eased away from the sluggish Powell and Gay before crossing the line in 9.75 seconds, one hundredth of a second off his world-leading time in 2015.
Twice Olympic champion Allyson Felix won the women's 200 metres before world record holder and Olympic champion David Rudisha, clearly hindered from a thigh injury suffered earlier this season, finished second in the 800 metres.
Olympic champion Christian Taylor of the U.S. won the triple jump with two leaps of 18 metres-plus while Keshorn Walcott was first in a thrilling javelin event with a meeting record throw of 90.16 metres.
(Reporting by Tom Hayward, editing by Tony Jimenez)
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