Aleksandar Mitrovic nodded Newcastle in front but Aguero’s brilliant burst of goals began when he headed City level.
It continued after the break when his deflected shot made it 2-1 and he ran through soon after for his hat-trick.
Kevin de Bruyne’s volley made it 4-1 before Aguero struck again with a curling shot and close-range finish.
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Newcastle, who are still without a league win this season, had chances to extend their lead after £13m striker Mitrovic scored his first goal since joining the club in the summer.
But Aguero’s virtuoso show – which ended his Premier League goal drought in style – means the Magpies fall to the bottom of the table on goal difference.
Aguero’s return to form
Going into the game, Aguero was without a goal in open play in 595 minutes in all competitions, and any Premier League goal in 424 minutes since City’s win over Chelsea on 16 August.
The 27-year-old Argentina striker’s shooting statistics were all well down on his usual high standards but when he returned to form, a shell-shocked Newcastle had no way of stopping him.
His early season frustration continued with his first two shots of the game both ending up off target, but his next five efforts all found the net.
The pick of the bunch was his fourth, which came when he looked up on the left-hand side of the area and picked his spot in the opposite corner.
It was something of a surprise when City manager Manuel Pellegrini chose to take him off, soon after he timed his far-post run to perfection to slide home De Bruyne’s cross for his fifth goal and City’s sixth.
Newcastle fans joined the applause as he left the field on 66 minutes – no doubt grateful he would not add to his tally – but, despite his early exit, Aguero still joined a select club of players to score five goals in a single Premier League game.
Pellegrini claimed afterwards that Aguero was injured, which makes his performance even more remarkable, but said he was not surprised by his haul of goals.
“Sergio Aguero is different,” Pellegrini said. “In other games he was maybe having a lot of chances but not scoring – today he returned to his normal amount of chances he creates, but this time he scored.
“He was not upset about going off. He was having treatment at half-time and it was a risk for him to finish the whole game.”
Before Saturday, Aguero had scored one goal in 482 Premier League minutes this season, with a shot conversion of 6.25%
Against Newcastle he managed five in 66 minutes, with a shot conversion rate of 71%.
Aguero touched the ball nine times between the 42nd and 62nd minutes and scored with five of them for the fastest five-goal haul in Premier League history.
Newcastle have now won only one of their past 19 league games, and their failure to find a victory in any of their first eight matches of this campaign makes this their worst start to a season since 1898-99.
The Magpies could take plenty of encouragement from their 2-2 draw with defending champions Chelsea last week, but it was difficult to see any positives in their complete collapse at Etihad Stadium.
Boss Steve McClaren tried his best, pointing out that his side could have been 3-0 up before City and Aguero responded, but admitted they had no answer to the Argentina striker after the break.
“You are coming up against a top-quality team,” McClaren told BBC Sport. “Aguero was world class. He is getting back to form and we were punished by a really high-quality opponent.
“It was such a magnificent performance in the first half. it was same against Chelsea last week but in 13 minutes we got beaten by world-class individuals. We probably frightened them into life and they killed us for it.
“We have had a tough eight games but I have seen enough in the last two weeks that we can win football matches.
“We were unlucky last week and this week. There is enough in there, we just need consistency. Our season begins now.”