Kerr jumped 2.32m to beat Ukrainian Oleh Doroshchuk by 2cm.
Kerr's winning height was just 1cm below his season best.
The Olympic champion had a few issues early on and missed a 2.22m jump before he found his form.
"Coming in, I was not sure what is coming. We were not sure with the weather and the conditions, so it was about trying to compete and I am glad I was able to do that and grab that win," Kerr said after the win.
"That is my first Diamond League overall victory so that means a lot for me and my career. I am very proud of what I did today.
"I had a few frustrating competitions but, with my team, we made sure that I am in a good shape now and I am pretty confident about my jumping at the moment. And in Tokyo, I am pretty sure that I will jump good as well."
Sprinter Zoe Hobbs finished sixth in the women's 100m.
Hobbs, who was the ninth qualifier, recorded a time of 11.09 seconds.
The race was won by Olympic champion Julien Alfred, of St Lucia, with a time of 10.76 seconds
On Thursday, Canterbury's Tom Walsh finished fifth in the men's shot put.
The world championships start in Tokyo on September 13.
