With just five games remaining, Grant's side still face a major challenge if they are to overhaul United, who face Middlesbrough on Sunday.
But with Sir Alex Ferguson's side still to visit Stamford Bridge, this result ensures the battle for the championship is by no means over despite the apparent unease at the club. By contrast, defeat was a massive blow to City's hopes of qualifying for Europe and manager Sven Goran Eriksson now faces a major task if he is to prevent the season ending in an acute sense of anti-climax.
Chelsea's midweek Champions League defeat to Fenerbahce in Istanbul had done nothing to ease the growing tension surrounding Grant's position and reports immediately before this game that the long-serving and popular assistant manager Steve Clarke is now looking to quit Stamford Bridge only reinforced the view that there are deep-seated problems at the club.
Against such a backdrop, Grant desperately wanted an early lift and that duly came after just six minutes when City captain and centre-back Richard Dunne put through his own goal.
With the vital return leg with Fenerbahce looming 72 hours later, Grant had omitted striker Didier Drogba from his 16-man squad but that did nothing to dilute Chelsea's firepower and a swift incisive early move involving Kalou, Michael Essien and Nicolas Anelka culminated with Dunne sliding Anelka's cross past his keeper Joe Hart.
That was precisely the start Chelsea needed and with City's form having apparently deserted them since the turn of the year, the London club should have taken control.
Eriksson's side have been in free-fall since mid-season when they still harboured hopes of a top-four finish and came into this game having won just three of their previous 15 league games and still painfully short of a consistent goal-scorer.
Indeed, Anelka's contribution to the opening goal will have been particularly frustrating for Sven-Goran Eriksson, the City manager, who this week lamented his failure to persuade Anelka to pass up the opportunity to join Chelsea and rejoin his former club when the Frenchman left Bolton in January.
Eriksson had heavily criticised his players following last weekend's dismal defeat at Birmingham but they showed considerably more spirit as they battled to cancel out Chelsea's lead in the remainder of the first half.
Martin Petrov twice came close from distance and only timely interventions from visiting defenders Juliano Belletti and Alex prevented City from drawing level.
The half-time interval, however, brought an abrupt end to City's response and in a brief three-minute spell Chelsea reasserted their authority by claiming another goal and should have put the game beyond reach.
The crucial second goal came eight minutes after the restart, a product of a series of one-twos between Kalou and Essien that prised open the City back-four and culminated with Kalou rounding Hart and stroking the ball into the empty net.
A minute later it should have been three when Anelka found space behind the home defence before Hart snuffed out the danger with an excellent save and the keeper denied the Frenchman again, tipping his header onto the bar and then reacting superbly to swat the ball off the goal-line.
The contest, though, was effectively over and Grant's side could afford themselves the luxury of coasting through the remainder of the game in anticipation of Tuesday's clash with Fenerbahce, knowing they were still well and truly in the title race.