Kimmons, the second-slowest qualifier for the final, surged from the start and outleaned his rivals at the finish line to win in 6.51 seconds with Powell, a world and Olympic 4x100 relay champion, second in 6.52, and American Michael Rodgers, the 2010 world runner-up at 60m, third in 6.53.
"I knew coming into this meet it was a great field," Kimmons said. "I just wanted to get off to a great start and execute my race."
Powell, who owned the world record from 2005 until 2008, when Usain Bolt broke the mark, tested positive for a banned substance in 2013. His ban ended last year.
Trinidad and Tobago's Michelle-Lee Ahye won the women's 60m crown in 7.15, edging American Tianna Bartoletta, a two-time world long jumpchampion, by .04 of a second with Ghana's Flings Owusu-Agyapong third in 7.26.
New Zealand's Nick Willis, the 2008 Olympic 1,500 runner-up, won the mile in 3:51.61, shattering the decade-old meet record of 3;43.18 by Kenyan Laban Rotich with the year's world-best time and a New Zealand record.
American Ben Blankenship was second in 3:53.13 with Morocco's Abdalaati Iguider, the 2012 world 1,500 champion, third in 3:54.41.
Ethiopia's Dejen Gebremeskel, the 2012 London Olympic 5,000m runner-up, won the 3,000 in 7:48.19, edging American Bernard Lagat by .14.
Ethiopian Dawit Seyaum, last year's world 1,500 outdoor junior champion, took the women's 2,000 in 5:35.46 with Kenya's Sally Kipyego, a 10,000m London Olympic runner-up, second in 5:40.35.
American Jenny Simpson, the 2011 world 1,500m champion champion, captured the women's two mile in 9:18.35.