Google-hangout

Google+Hangout button makes it easy to implement.

The invites provided in the button parameters allows you to invite specific users to hangout in one of the following formats:

• Google+Profile ID
• Google+Circle ID
• Email Address
• Phone number

It's just an invitation, so you need to click the "Invite" button in the dialog that appears, but you can almost accomplish your goal.

Note:
https://developers.google.com/+/hangouts/button#inviting_people_to_the_hangout

For example, here is an example JavaScript code to invite by email address:

gapi.hangout.render("ID you want to render buttons", {
    render: "createhangout"
    invites: [{
        id: "Email address I want to invite"
        invite_type: "EMAIL"
    }]
})