Wow, replace the age of your daughter with age 7, and I could have written your post. I almost did a month ago.
It seems your daughter has a similar issue to mine, in that she massively overreacts to a situation. A month ago I sent my daughter to bed 5 minutes early after she did something she shouldn't have and then shouted at me. We had further shouting at me, stamping feet, throwing and kicking things and screaming, this went on for 50 minutes (40 minutes while she was in her room)! I genuinely didn't know what to do. I eventually ended up closing my bedroom door and crying. So naturally, this led to me reconsidering what I could have done differently.
Since then, we have had a few other mini versions. I have worked out a way to stop it, it works for my daughter. When a situations begins to go the wrong way, I get very close to her, hold her close so she is looking at me, and tell her to stop and explain in very simple words how her actions are making the situation worse, and explain to her the alternatives, at this point she usually starts crying as she cannot cope with the emotions inside her. She then cuddles me and will then serve out her punishment (usually a 7 minute timeout). Afterwards, she comes to see me, apologises and gives me another cuddle.
I put it down to simple emotional immaturity. She is lacking the coping mechanisms to deal with her emotions when things don't go her way. I am sure that by 7 she should have grown out of it, but emotionally she has always been behind her peers. Perhaps though, had I addressed this earlier, I could of helped her. This seems to be working now. These massive blow ups have been less frequent, they were 3 or 4 times a week at their worst, and we are down to them being weekly.
I am not claiming that this will work for you, I am no expert and not a master at this parenting thing. My husband and I am just learning as we go, without support or guidance as we are not close to our extended family. I came to this approach after recalling a conversation with another parent I met briefly who told me, that sometimes the most difficult behaviour comes out of a lack of security, and that she had done this with her 13 year old after a similar meltdown. It sounded crazy at the time...
Good luck.