Watford led 2-0 at half-time courtesy of goals from Fernando Forestieri and Troy Deeney, but City rallied after the break as Aguero's treble was complimented by Aleksandar Kolarov's fortuitous strike to spare Manuel Pellegrini's side's blushes.
Giuseppe Sannino's men were rewarded for a fine opening period with two goals. First the impressive Forestieri showed a good turn of pace before finishing neatly from the left, before Troy Deeney capped a swift Watford breakaway.
After a lacklustre opening, City showed a marked improvement after the break and halved the deficit through Aguero's tap-in before he curled home a second with his left foot.
And the comeback was completed by quickfire goals from Kolarov and Aguero in the closing stages to stun the Championship side.
City opted not to risk Alvaro Negredo with the Spaniard nursing a shoulder injury so Edin Dzeko started, while Watford defender Lloyd Doyley replaced the suspended Fitz Hall.
The hosts uncharacteristically struggled to maintain possession in the early stages, but fashioned a good opportunity after 11 minutes when Kolarov flicked Jesus Navas' corner invitingly across goal and just beyond the reach of Joleon Lescott.
Watford dealt well with City's attacking force and deservedly went in front after 21 minutes, when Forestieri outpaced Martin Demichelis before calmly slotting under Costel Pantilimon in the City goal.
City responded and almost equalised when Yaya Toure released Sergio Aguero, who swivelled in the box and saw his shot deflected wide.
But things went from bad to worse for the home side on the half-hour mark as Watford doubled their lead.
Demichelis played a poor pass out of defence and Sean Murray found Ikechi Anya, who picked out Deeney and the striker kept his composure to sidefoot home from six yards.
A slick move on the stroke of half-time created the opportunity for a third goal, but Daniel Pudil's fierce effort found the side-netting.
City showed much more energy and drive after the break and Dzeko fired straight at Jonathan Bond from 10 yards when slightly off balance.
The deficit was reduced after 58 minutes, when Kolarov's teasing cross was met by a sliding Dzeko and, though his effort was saved, Aguero was on hand to convert the rebound.
Roared on by an expectant home crowd, City poured forward with Dzeko again testing Bond, then substitute Stevan Jovetic had an effort closed down with 20 minutes remaining.
Watford's resistance finally broke in the 78th minute. Navas drove forward and picked out Dzeko, who in turn laid into the path of Aguero and the striker curled the ball into the top corner from the right-hand side.
The comeback was complete in the 85th minute when Kolarov's hopeful 30-yard strike squirmed under the despairing Bond.
And there was still time for a fourth goal as Aguero completed his hat-trick with a back-post header.
