Manuel Pellegrini admitted the champions were in the midst of a crisis of confidence following their latest European defeat and QPR seemed determined to increase City's misery at Loftus Road.
Charlie Austin scored the opening goal after finding the City net for the third time after 21 minutes.
Austin had two strikes ruled out in the space of 30 seconds after eight minutes, but each time the visitors' shambolic defence was reprieved.
He was offside in heading in, then City goalkeeper Joe Hart kicked the ball twice, firstly with his standing foot, before the striker scored
Referee Mike Dean correctly ruled out the effort.
Hart made a stunning save from Austin after 14 minutes before it was fourth time lucky as the striker ghosted in behind an absent City defence, was played on by Eliaquim Mangala, and finished clinically for his sixth of the season.
Aguero, who was excellent throughout, was given the benefit of the doubt by the officials when he equalised, despite the possibility of the strike being ruled out for offside and handball.
Austin's cross was then turned into his own net by Martin Demichelis but Aguero mesmerised the QPR defence for a second time to earn a draw.
Third-placed City now have one win in six games and are eight points behind leaders Chelsea, who won at Liverpool earlier on Saturday, entering the international break.
City made four changes following the midweek defeat to CSKA Moscow which leaves their Champions League future teetering on the edge, with Mangala replacing injured captain Vincent Kompany.
Samir Nasri had an effort blocked, Aguero fired over, as did Yaya Toure, before QPR responded.
Austin was offside when converting Eduardo Vargas' cross.
From the resulting free-kick, Hart's standing foot touched the ball before he cleared straight to the striker, who fired in.
Had it been anywhere else on the field, it would have resulted in an indirect free-kick to QPR, but as it happened inside the area, Law 13 determines the ball was not in play and Dean made the right call.
It was reminiscent of a bizarre moment involving Rob Green at West Ham last month, when Enner Valencia had a strike ruled out after the QPR goalkeeper passed him the ball.
Austin was denied again, this time by a stunning Hart save, after Bobby Zamora had unsettled Mangala to lay off Karl Henry's cross.
QPR continued to press, with Sandro's volley blocked by Sagna, and gained their rewards when Mangala played Austin onside.
Mauricio Isla fed the striker, who finished with aplomb for his fourth goal in three games.
"Austin for England" was the call from the QPR support in front of the watching Roy Hodgson.
Toure fired narrowly over as he tried to spark his side into life.
The visitors were soon level, although Rangers had reasons to feel aggrieved as Aguero was offside when Mangala launched his long pass.
Aguero pulled the ball down, it brushing his arm as he did so, before twisting and turning Steven Caulker and tucking in.
Green's protests made little difference.
Toure shot wide and Dunne was perhaps fortunate to only be booked for a heavy challenge on Nasri as City poured forwards again, but by the interval they were indebted to a further stunning Hart stop.
The England goalkeeper denied Austin after Fernando's air-shot.
A frenetic resumption saw Toure unable to convert Nasri's cross along the goalline before Leroy Fer's shot deflected off Demichelis and narrowly wide at the other end.
Toure's cross was then just out of reach of Aguero and Fernando made a crucial interception with Austin's cross destined for Zamora.
Dunne was fortunate to avoid a second booking for raising his leg towards Fernando when competing for an aerial ball, although the free-kick was given in QPR's favour.
Edin Dzeko made a three-minute substitute appearance in place of the anonymous Fernandinho before limping off with a calf problem
Frank Lampard came on in his place.
Lampard has had a habit of making an impact for City, but this time his side found themselves behind with 14 minutes remaining.
Austin turned provider, delivering a devastating ball from the right wing towards Zamora which Demichelis could only turn in.
The lead might have evaporated when half-time substitute Joey Barton headed back towards Green following the goalkeeper's poor kick.
Aguero almost capitalised, only for Dunne to clear off the line.
City stepped up a gear
Substitute James Milner had a header cleared off line by Caulker, Green saved from Toure, Sagna flashed wide across goal and then the visitors equalised.
Toure found Aguero, who again bamboozled the QPR defence before firing in past Green and three defenders.
Both sides pushed for a winner which never came.
Source : PA
Source: PA