Vidic watched on as his fellow Serbian battled through a tough match against Tomas Berdych this afternoon, eventually winning 7-6 6-4 6-3 to book his place in the semi-finals.
Djokovic was happy that such a successful compatriot watched him win, and revealed that he would invite him back for the semi-finals to act as a lucky charm again.
"He's a lucky charm. I'll make sure he's there [for the semi-final]. We wanted to invite Nemanja because he's one of the most successful and most recognised Serbian people in the world," PA Sport quotes Djokovic as saying.
"He accepted that, and he said he would be here in these days. I was very much delighted to see him in our box today and watching the match and supporting me.
"It's the first time he actually came to watch me. I've watched him before in the national team a few times. We met briefly. He plays for one of the best teams in the world. I was just very happy to see him there in the stands and supporting me."
Djokovic will face Juan Martin del Potro in the semi-final on Friday.