The Argentina international glanced home a 15th-minute header, albeit one which should have been ruled out for offside, to reach his century in 147 appearances, a feat bettered only by Geordie hero Alan Shearer.
However, a 31st-minute equaliser from Vurnon Anita snatched a 1-1 draw which leaves City five points clear of fifth-placed Manchester United and Rafael Benitez’s men two from safety with four games remaining.
“I am happy. We started winning the game but we could not have the control after that. We knew that it was very tough,” said City boss Manuel Pellegrini.
“The officials have nothing to do with the result. I didn’t see the team with the energy from Saturday, but we play after three days at the end of the season and it is not easy for the team to recover.
“We are just trying to add points. Sergio Aguero’s record is deserved, he makes an important difference for us. I am happy for him. Vincent Kompany played well, he played 90 minutes and he was OK.”
Like Pellegrini, Magpies boss Benitez was reasonably happy with a point.
“I have to be pleased because against a team like Man City, to do what we have done from 1-0 down, the reaction of the team, you have to be pleased.
“I haven’t seen the replay of Sergio Aguero’s goal but they tell me he was offside. You can not change anything. I think they should get it right but we cannot change it. That’s it.
“The team has more belief now, the fans are behind the players, and they will fight to the end. Today was an example of that.
“Vurnon Anita is very clever, he knows when he has to go forward. The players are doing what they have to do, they are playing with passion, with the commitment that the fans expect.”
Having taken the decision to drop January signing Jonjo Shelvey for Saturday’s victory over Swansea, Benitez sent summer acquisition Georginio Wijnaldum to join him on the bench, the first league game the Dutchman had failed to start this season.
With Vincent Kompany back at the heart of the City defence, however, the victory the Spaniard so desperately needed looked a tall order, and the task became even sterner within 15 minutes of kick-off.
The visitors, as expected, had enjoyed the greater share of the possession, and although Papiss Cisse headed over from an inviting fourth-minute Andros Townsend cross, they took the lead in controversial circumstances.
Townsend was aggrieved to have been penalised for his challenge on Aleksandar Kolarov, and his disappointment increased markedly when the Serbia international drilled the resulting free-kick to the near post and Aguero rose to glance it past keeper Karl Darlow with the officials failing to spot that he did so from an offside position.
Kevin de Bruyne was at the centre of most of City’s best work as they looked to kill the game off as quickly as possible, although he blazed wastefully wide after Jamaal Lascelles’ misplaced 23rd-minute pass.
But Newcastle eventually responded and should have been level six minutes later when skipper Moussa Sissoko ran on to Kolarov’s equally ill-judged pass and burst past Kompany, only to shoot tamely at keeper Joe Hart.
The Frenchman did play a key role as the home side got themselves back on terms 14 minutes before the break. He collected Townsend’s pass on the left and floated a crossfield ball out towards Anita, who cushioned it into his path before cutting inside and drilling left-footed past Hart and in off the base of the far post.
Ayoze Perez found himself unmarked inside the visitors’ penalty area three minutes after the restart, but he could not climb high enough to meet Townsend’s clever free-kick.
Aguero saw muted penalty appeals waved away after he went to ground under Chancel Mbemba’s challenge two minutes later and Darlow got down well to turn away Jesus Navas’ strike as City slipped into top gear once again.
It took a brave header from Pablo Zabaleta to deny substitute Aleksandar Mitrovic as he tried to get on the end of Townsend’s cross after Cheick Tiote and Sissoko launched a lightning break on the hour, but Darlow needed two attempts to collect Aguero’s snapshot as City hit back three minutes later.
Darlow had to beat away De Bruyne’s blistering 74th-minute drive as the game entered its final stages, but Magpies substitute Wijnaldum might have won it at the death after robbing Kolarov, only to be denied by Hart.
Darlow, Anita, Mbemba, Lascelles, Dummett, Tiote, Colback, Townsend (Wijnaldum 81),Sissoko, Perez (Aarons 90), Cisse (Mitrovic 55).
Hart, Zabaleta, Kompany, Mangala, Kolarov, Toure (Fernandinho 73), Fernando, Jesus Navas (Bony 84), De Bruyne, Delph (Sterling 68), Aguero.