The Citizens were dominant throughout the 192nd Manchester derby, but they were behind at the break after Marcus Rashford fired a stunning 25-yard strike in off the crossbar in the eighth minute.
Pep Guardiola's men eventually prevailed in the second half, though, with local lad Phil Foden inspiring the reigning champions to victory with two superb strikes, arrowing his first into the top corner 10 minutes after the interval before slotting his second beyond Andre Onana on the 80-minute mark.
Erling Haaland somehow missed a sitter from just a few yards out on the stroke of half time, but the Norwegian made amends in second-half stoppage time as he met Rodri's through-ball to place a composed finish into the bottom corner, securing three crucial points for the Citizens as well as the bragging rights over their bitter rivals.
Man City's victory has extended their impressive unbeaten run across all competitions to 19 matches, while it was also the first time in their history that they came from behind to beat Man United in a Premier League game, having failed to do so in 28 previous attempts (drawing three and losing 25).
After securing a comfortable 3-0 win at Old Trafford earlier this season, the Citizens have also completed their sixth Premier League double against the Red Devils, more than any other team in the division's history.
In addition, City have now scored in 55 consecutive home matches across all competitions, equalling a club record set between 2012 and 2014.
Meanwhile, midfield maestro Rodri - who played the full 90 minutes at the Etihad - has set an all-time English football record after helping the Citizens claim maximum points over Man United.
Indeed, the Spaniard has extended his remarkable unbeaten run in all competitions to 59 games, surpassing the previous record held for 16 years by former Chelsea defender Ricardo Carvalho (58).
Rodri's record was momentarily under threat on Sunday as Man United were in front for 55 minutes, but City's comeback victory means that the midfielder now boasts an impressive 76.3% win rate during his 59-game undefeated streak, which includes 45 victories and 11 draws.
The 27-year-old last tasted defeat in February last year when the Citizens suffered a 1-0 top-flight defeat away against Tottenham Hotspur.
Man City's win over Man United has boosted their Premier League title hopes as they have moved to within one point of leaders Liverpool, who welcome Guardiola's men to Anfield for a top-of-the-table clash next Sunday.