United had all the possession but failed to make it count against a Reading side who had substitute striker Dave Kitson red-carded in the 72nd minute, less than a minute after coming on, for a reckless tackle on Patrice Evra.
Chelsea, looking to wrest the title back from United this season, took the points at Stamford Bridge with a second-half strike from Ghana midfielder Michael Essien.
Victory was made even sweeter by Chelsea setting an unbeaten home record in the top flight of 64 games. The run dates back to February 2004 and eclipses the previous mark set by Liverpool from February 1978 to January 1981.
In the day's first match, Arsenal snatched a late 2-1 victory at home to Fulham. Dutch striker Robin van Persie equalised with an 83rd minute penalty and Belarus midfielder Alexander Hleb struck a 90th minute winner.
The day's action left United as the only one of England's big four without a winning start. Liverpool beat Aston Villa 2-1 on Saturday with a fine late strike by captain Steven Gerrard.
Along with the dropped points, United also lost England striker Wayne Rooney to injury for the second half.
Manager Alex Ferguson was already without fellow strikers Louis Saha and Ole Gunnar Solskjaer through injury, while new Argentine signing Carlos Tevez was also missing.
Ferguson's men also came up against an inspired Reading keeper in American Marcus Hahnemann.
There was no shortage of goals, though, in west London, where Birmingham took a shock lead with a 15th minute header from Finnish, former Chelsea striker Mikael Forssell.
The hosts hit back with goals from league debutants Claudio Pizarro of Peru and Frenchman Florent Malouda, who was on target again after scoring in last Sunday's Community Shield defeat by United.
City levelled with a left-footed, bullet strike from their new French signing Olivier Kapo, but Essien gave Chelsea a deserved victory with a curling first-time shot from Shaun Wright-Phillips's cut-back.
Chelsea coach Jose Mourinho told BBC Five Live radio: “We had so many chances to kill the game, it would have been more enjoyable for me to see a 4-2 or a 5-3 than a 3-2.”
But he added: “It was a good game to celebrate the home record, a game with goals and enthusiasm, and better than a 0-0 where we still have the record but it's not a good game.”
Mourinho, whose side have suffered a spate of injuries, was without captain and central defender John Terry, but was able to send on Ivorian striker Didier Drogba from the subs' bench.
Over at the Emirates Stadium, a goalkeeping howler by Arsenal's Jens Lehmann gifted Fulham the lead in the first minute, the German's fluffed clearance leaving the visitors' new Northern Ireland striker David Healy a tap-in on his competitive debut.“Better late than never,” Arsenal manager Arsene Wenger told BBC radio after his side's late strikes. “We were physically and mentally strong and didn't give up.
“That kind of result can change a season for a team, and certainly strengthen the belief.”
Meanwhile, a stunning 87th-minute free kick by captain Steven Gerrard gave Liverpool a 2-1 victory at Aston Villa on Saturday.
Sven-Goran Eriksson's Manchester City beat West Ham United 2-0, Roy Keane's promoted Sunderland snatched a 1-0 win over Tottenham Hotspur and Sam Allardyce's first game as Newcastle United boss ended in a 3-1 win at former club Bolton Wanderers.
Liverpool looked set for a disappointing start when their 31st-minute lead, courtesy of an own goal by Villa's Danish defender Martin Laursen, was cancelled out by Gareth Barry's 85th-minute penalty.
But Gerrard curled home an inswinging free kick from 25 metres two minutes later, dipping the ball into the top right-hand corner after deftly bending it around the Villa wall.
Manchester City's goals came from new signings, following the takeover by former Thai Premier Thaksin Shinawatra, with Italian striker Rolando Bianchi and Brazilian midfielder Geovanni on target.
Sunderland's winner came from new signing and substitute Michael Chopra in the fourth minute of stoppage time.
There was no room for sentiment for Allardyce on his return to the Reebok Stadium.
His side were 3-0 up in under half an hour, with Nigerian striker Obafemi Martins scoring twice, as they swept aside a Bolton side managed by his former assistant Sammy Lee.
Elsewhere, Blackburn Rovers came from behind to beat Middlesbrough 2-1, Everton were 2-1 winners over Wigan Athletic and promoted Derby County drew 2-2 with Portsmouth.
Results:
Played on Sunday:
Arsenal 2 Fulham 1
Chelsea 3 Birmingham City 2
Manchester United 0 Reading 0
Played on Saturday:
Aston Villa 1 Liverpool 2
Bolton Wanderers 1 Newcastle United 3
Derby County 2 Portsmouth 2
Everton 2 Wigan Athletic 1
Middlesbrough 1 Blackburn Rovers 2
Sunderland 1 Tottenham Hotspur 0
West Ham United 0 Manchester City 2
—Reuters