Mariah Carey -- NBC Gambles ... She Is Performing Live

NBC just realized Mariah Carey is worth the hassle ... because they have now booked her to perform live tonight ... this after pulling the plug on her Tuesday night.

TMZ broke the story that Mariah showed up more than 3 hours late for a taped performance that was supposed to air during the Christmas tree lighting ceremony Wednesday night in Rockefeller Center. She was delayed because she was yacking with her lawyer about the divorce settlement with husband Nick. When she finally showed up, frustrated NBC execs sent her packing.

But, NBC had a change of heart and they are now rolling the dice that she will show up tonight. It's interesting ... the decision comes after LeAnn Rimes tweeted that she would have more air time, insinuating it was because of 'the Mariah problem.'

The tree lighting ceremony just got more interesting.

Mariah tweeted about the ordeal Wednesday afternoon, writing, "Last night's situation was beyond my control. I apologize to all that showed up, you know that I would never want to disappoint you."