Aguero was the headline act in a memorable encounter as Manuel Pellegrini's second-placed team kept up the pressure on leaders Chelsea.
The Argentina forward opened the scoring in the 13th minute, and then struck from the penalty spot seven minutes later after Christian Eriksen's 15th-minute equaliser.
Referee Jon Moss awarded the third penalty of the match in the 62nd minute when Martin Demichelis tripped Tottenham's Roberto Soldado. However, replays showed the offence took place outside the penalty area. Justice was served when Spanish striker Soldado fluffed his lines, with Joe Hart producing a fine save low down to his right.
Moss awarded his fourth penalty of the night in the 68th minute, when debutant Federico Fazio pulled back compatriot Aguero, to also earn himself a straight red.
Aguero, who is now City's all-time record scorer in the Premier League, stroked home the penalty and sealed the one-man demolition job with another clinical strike to make it four in the 75th minute.
"I'm very happy," said Aguero. "We are all really happy. The [man of the match] trophy is for all the team because the team has helped me get the goals."
The English league record for penalties in a single game is five, awarded by referee Kelvin Morton when Crystal Palace met Brighton in March 1989.
Rodgers backs Sterling to answer critic
Liverpool manager Brendan Rodgers expects Raheem Sterling to silence the critics as the Liverpool midfielder looks to put a difficult week behind him when his side play QPR on Sunday.
Sterling endured some unpleasant jibes after telling England manager Roy Hodgson he felt too tired to start last weekend's Euro 2016 qualifier against Estonia.
"I've obviously read and listened to a lot of what has been said," said Rodgers. "He [Sterling] has been absolutely incredible for me and what has been nice to see is his maturity as a young man.”
Meanwhile, much to the agony of Rodgers, England striker Daniel Sturridge is set to be sidelined for another month.
Sturridge has already been out of action for six weeks due to a thigh strain he picked up on international duty.
The 25-year-old had hoped to make his comeback today but the former Chelsea forward pulled his calf during training on Thursday and could now be absent for up to another month.
"Sturridge has pulled his calf," said Rodgers. "He's looking at being out for another two to four weeks. It's a big blow as we were looking forward to welcoming him back. He has worked tirelessly.”
Meanwhile, in the other match of the day, Stoke City will take on Swansea City at the Britannia Stadium.
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