Medved (Е), that's the right direction.

There is also another specific meaning. And the Eng. verb 'chat up' is used for it.

Chat up – To chat someone up is to try and pick them up. If you spotted a scrummy girly in a bar you might try to chat her up. Or a girl might try and chat up a chap!
source for Brit.Slang http://teacherluke.co.uk/2013/09/12/148-british-slang-a-to-c/

So sometimes разговорить may be used for such a situation. I am not sure this is the exact equivalent, but it makes sense to compare разговорить and 'chat up'.