The match had looked on course to end in a stalmate, with top-drawer saves from David De Gea and Ben Foster the highlights before Rodriguez's goal from a corner handed a third Premier League crown to City. "Premier League Champions 17/18", City posted on their official Twitter account.
A serial victor as a manager with Barcelona and Barcelona, Guardiola ended his first year in England at City without silverware - his only failure to win a trophy since his managerial career started back in 2007.
Manchester City are now 16 points ahead of 2nd placed side Manchester United - the Premier League record points gap between 1st and 2nd place at the end of a season is now 18 points by Manchester United in 1999-00.
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For Manchester City, whose manager Pep Guardiola had promised to play golf with his son rather than watch the game at Old Trafford, it was an odd end to the weirdest fortnight of their season.
Soon after United " s defeat on Sunday, the City website tweeted: "Our Time.
That defeat came in between two losses to Liverpool as they were knocked out of the Champions League at the quarter-final stage.
City captain Vincent Kompany said: "It's the same feeling as the first time and you can't describe it". We always gave them the opportunity to be solid, compact in the low block with strong physical players. Here are some of the most impressive stats from their title win.
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As for City, it has a month to finish a season with the most points, goals and wins in a single Premier League campaign.
"We had a few days to rest and prepare but football is unpredictable and sometimes things happen".
The English forward headed home in the 73rd minute to seal a stunning victory at Old Trafford for the Premier League's bottom club.
United manager Jose Mourinho had long given up hopes of winning the title, instead focusing on finishing second.
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"This one differs in that we were consistent the whole season and we were able to play at the level we're expected to perform at".