Baker, winner at the Eugene meeting last Saturday, set the fastest time this year as he won in 9.93 seconds ahead of Frenchman Jimmy Vicaut, the European record holder, and Italian Filippo Tortu.
Coleman, who beat Jamaican great Usain Bolt into third place at the world championships in London last year when he was runner-up to Justin Gatlin, was fourth.
Timothy Cheruiyot avenged his defeat by fellow Kenyan Elijah Manangoi at the worlds by winning the 1500m in 3 minutes 31.22 seconds, more than two seconds clear of the world champion.
World silver medallist Marie Jose Ta Lou of the Ivory Coast pulled away down the home straight for a convincing win in the women's 200m ahead of Bulgarian Ivet Lalova-Collio.
"I'm happy that my winter went well but I feel more confident over 100 metres - the 200 metres is becoming too long for me," said Ta Lou.
"I'm surprised to still be running well after changing my technique recently but now I need to maintain it. I still need to work on my start and finish."
(Writing by Brian Homewood in Bern; Editing by Ken Ferris)
