City were not at their all-action best early on as Burnley looked comfortable at the back, but the game turned on a penalty decision that incensed the visitors when Bernardo Silva was adjudged to have been brought down by Burnley goalkeeper Nick Pope just before the half hour.
The list of guests included celebrities from across the globe, politicians, the who's who of Hindi and south Indian cinema world and almost all the top cricketers of the country.
A summary of Tuesday's League Cup matches.
Holders and Premier League leaders Arsenal will be at home to Championship (second tier) Burnley in the fourth round of the FA Cup after most of the big guns avoided top flight opponents in Monday's draw.
Saturday's clash between Manchester United and Tottenham Hotspur at Old Trafford is already shaping up as an early-season eliminator to challenge runaway leaders Manchester City for the Premier League title.
Premier League Swansea City fell victims to the first major giant-killing of the FA Cup third round on Sunday when they lost 3-2 away to League Two (fourth tier) side Oxford United.