The hosts' Argentine front man added two more goals to his first half haul after his fellow countryman was shown a straight red card midway through the second period.
Aguero and Roberto Soldado both had penalties saved earlier in the game - Soldado's spot kick could have levelled it up at 2-2 - with Christian Eriksen having bagged his second goal in as many matches to cancel out Aguero's opener.
Mauricio Pochettino made a few changes after the international break, with Fazio being awarded a Premier League debut in central defence alongside Younes Kaboul and Eric Dier stepping in for the injured Kyle Naughton at right back.
Soldado returned in attack in front of an unchanged attacking three of Nacer Chadli, Christian Eriksen and Erik Lamela.
There was a gilt-edged chance to take the lead after a superb passage of play seven minutes in. Lamela seized possession on the edge of the area and travelled in the direction of Soldado before leaving it for the Spaniard, who dispatched a superb delivery to the oncoming Ryan Mason. The midfielder was clean through on goal and only the legs of Joe Hart denied an advantage being taken.
Chadli then embarked on a mazy run and played in Eriksen, who smashed narrowly over via a deflection. David Silva was beginning to cause problems at the other end and Hugo Lloris, with a little help from Kaboul, did well to foil a pinpoint low cross that would have resulted in a clear shooting chance.
On 12 minutes there was a lesson in clinical finishing when Aguero collected the ball to the right of the area and simply stepped inside and unleashed a low drive beyond the dive of Lloris and into the bottom corner of the net.
Two minutes later there was an emphatic response when Ryan Mason dispossessed a dithering Fernando in his own half. Soldado sprinted goalwards and played into the run of Eriksen, who found the net via the legs of a despairing Hart.
On 18 minutes City were awarded a penalty by referee Mr Moss after a coming together between Lamela and Lampard in the area in which Lampard went to ground. Aguero slotted home the spot kick.
Lloris then denied Aguero a third with a smart low save before Eriksen flashed a free-kick narrowly over the bar just before the half-hour mark.
A minute later Kaboul was adjudged to have tripped Silva and again a penalty was awarded, but this time Lloris saved from Aguero with his legs and the rebound thankfully flew over the bar.
Aguero then twisted Kaboul inside out before being foiled again by Lloris.
Eriksen stung the palms of Hart at the other end after superb approach play from Soldado. Hart again denied a leveller, this time from Mason, after Soldado and Eriksen initially unlocked the defence.
Jesus Navas had a chance on 44 minutes that Lloris diverted over the bar as we neared the end of an enthralling half of football in which the team gave an excellent account of themselves as a clever attacking force.
Aguero smashed in a fierce drive three minutes into the second half that Lloris somehow scooped away as City dictated the tempo of the opening exchanges following the restart.
Chadli was not too far away with a speculative volley on 56 minutes as changes were being readied in the technical area. There was a penalty shout as an Eriksen shot was body-blocked, as momentum was building among the men in black.
Lloris was forced to save from Navas at the near post as City sought to regain the upper hand, while a Silva ball squirted across the face of goal.
Andros Townsend and Mousa Dembele took over from Capoue and Lamela on the hour and a minute later Soldado was felled by Martin Demichelis and a third penalty of the game was awarded - and a second one was thwarted as Hart dived to his right to deny Soldado.
Hart then saved again from a Soldado volley from a whipped low cross from Danny Rose.
The game swung on 66 minutes when Rose headed backwards and Navas gave chase and kept the ball in play. When the Spaniard centred in the direction of the on-rushing Aguero, Fazio impeded his run and a fourth penalty was awarded. This time there was also a red card for Fazio and Aguero got his hat-trick.
Jan Vertonghen was introduced in place of Mason to try and shore up with the defence being a man short.
Aguero got his fourth in the 75th minute, breaking away beyond Vertonghen, cutting inside and cooly planting in the bottom corner.
We continued to try and get forward, Townsend's stoppage time free-kick hitting the top of the wall as an all-action game reached its conclusion.
City: Hart; Sagna, Kompany, Demichelis, Clichy; Navas, Fernando (Toure, 77), Lampard (Fernandinho, 28), Milner; Silva (Jovetic, 70); Aguero. Substitutes (not used): Caballero (GK), Kolarov, Boyata, Dzeko.
Spurs: Lloris; Dier, Fazio, Kaboul (C), Rose; Capoue (Dembele, 60), Mason (Vertonghen, 69); Chadli, Eriksen, Lamela (Townsend, 60); Soldado. Substitutes (not used): Vorm, Stambouli, Adebayor, Kane.
Goals: City - Aguero (13, 20 pen, 68 pen, 75). Spurs - Eriksen (15).
Yellow cards: City - Navas. Spurs - Mason, Dier.
Red card: Spurs - Fazio.
Referee: Jonathan Moss.