Did you see this post by any chance?
I am sure you need something for vCenter 5.5 or higher, while the post above is talking about vCenter 5.1 based SSO, but see if it still gives you some inputs.
The way I do it is, login in both the clients (VI Client and Web Client) everyday.
Did you happen to see vSphere HTML5 Web Client - this is included as official support in 6.5 release but until than something to explore.
There's also a similar discussion on following thread