Sven-Goran Eriksson's side made it five wins in a row to remain in third place in the Premier League.
Chris Riggott put through his own goal early in the game and two further strikes from Elano helped them continue their impressive start to the campaign.
Indeed, City's worst enemies were themselves as they started the second half sloppily and were lucky not to allow Boro a foothold back into the game.
City could not have wished for a better start when the unlucky Riggott deflected Martin Petrov's corner past keeper Mark Schwarzer from a couple of yards.
Boro enjoyed plenty of possession in the opening half hour but, with three strikers injured, lacked a cutting-edge, although Lee Cattermole's header brought a fine save from Joe Hart.
City doubled their lead in the 33rd minute when Brazilian Elano started and finished a slick passing move with a terrific shot from 25 yards after running onto a cheeky back-heel from Michael Johnson.
Boro started the second half with great spirit as City kicked off as though they already had victory secured.
And they had a rude awakening as Boro striker Tom Craddock - making his first Premier League start - twice went close, while Luke Young was also inches away from pulling a goal back.
Luckily for City they escaped because Boro had no attacking bite.
And the near misses provided a wake-up call for City who eventually regained their focus.
They made absolutely certain of victory in the 63rd minute when Elano struck again after curling a free-kick over the defensive wall and into the top corner of the net.
And City would have added a fourth goal but for keeper Schwarzer who brilliantly denied Stephen Ireland and kept out another decent striker from Petrov.
But it was Boro who belatedly got onto the scoresheet through a last minute goal from substitute Ben Hutchinson.
Hart parried a fiercely struck shot from Sanli Tuncay and Hutchinson was on hand to fire home the rebound which was only the second Premier League goal City had conceded at home this season.
While City celebrated another fine win, Boro were dragged even closer to the relegation places having picked up only one point from a possible 12 from their last four league matches.