Roberto Mancini's side, who snatched the title in the dying seconds of last season, again displayed the knack of scoring late as Barry's controversial effort broke Reading's resistance and moved City to within three points of United.
City have 39 points from 18 games, followed by four clubs on 30 points after a rainswept opening to the busy holiday programme yielded just 14 goals.
Everton climbed to fourth, making light of Marouane Fellaini's absence through suspension to win 2-1 at West Ham United in a game in which both sides ended with 10 men.
West Bromwich Albion also reached the 30-point mark after ending Norwich City's 10-match unbeaten league run with Romelu Lukaku sealing a 2-1 victory 10 minutes from time after Norwich had taken the lead at the Hawthorns.
Liverpool were the day's biggest winners, crushing a woeful Fulham side 4-0 at Anfield in the evening kick-off. Martin Skrtel, Steven Gerrard, Stewart Downing and Luis Suarez hoisted Brendan Rodgers's side up to eighth with 25 points.
QPR's revival under new manager Harry Redknapp came to a halt with a 1-0 defeat at Newcastle United while Sunderland edged clear of the bottom three after a 1-0 win at Southampton.
"I hoped, always. It was difficult. We had lots of possession but if you don't score early it is very difficult," Mancini told Sky Sports.
"You have to be patient but if we had scored one goal in the first half it would have changed the game. You need to score quickly in these games and sometimes you take a risk to score. I think we deserved to win.
"Our fans know we try until the last seconds always."
'PLAIN WRONG'
