Savery threw the final two scoreless innings in Sunday's 13-3 win, giving up two hits and walking one.
"He's going to fly back and [the doctors will] induce [labor] tomorrow," manager Bob Melvin said. "We'll cross our fingers for him. This is his first child. We're all excited for him."
Stephen Ellsesser is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.