WebForm_DoPostBackWithOptions is not defined using chrome
The respective JS code (i.e. WebForm_DoPostBackWithOptions(options)) is a built-in part and is linked dynamically. A proper URL is being generated by ScriptManager of the page.
Considering you've mentioned you're using URL Rewrite, try checking whether URLs like WebResource.axd?d=XXX are not being ignored/re-wrote.
Also, it might worth to look at IIS Handlers Mapping configuration to ensure .axd resources are mapped to the standard ISAPI module handler.
There is a bug in the browser definition files that shipped with .NET 2.0 and .NET 4, namely that they contain definitions for a certain range of browser versions. But the versions for some browsers (like IE 10) aren't within those ranges any more. Therefore, ASP.NET sees them as unknown browsers and defaults to a down-level definition, which has certain inconveniences, like that it does not support features like JavaScript.
Fortunately,A hotfix is available for .NET Framework 4.0
https://support.microsoft.com/en-gb/kb/2600088
You can read more about this issue on Scott Hansellman's blog