Rodri's late equaliser extended Manchester City's year-long unbeaten record at home but a 1-1 draw against Chelsea on Saturday handed Liverpool and Arsenal a huge boost in the Premier League title race.
Raheem Sterling gave Chelsea a first-half lead on his return to the Etihad and City were headed to a first defeat on home soil for 34 games until Rodri's deflected effort seven minutes from time.
City move four points behind leaders Liverpool and two adrift of Arsenal, but have a game in hand on both their title rivals.
A 3-1 Champions League win in Copenhagen in midweek was City's 11th consecutive victory in all competitions as they appeared well set to defend the treble of Premier League, Champions League and FA Cup they won last season.
But Chelsea exposed chinks in the champions' armour.
City have kept just seven clean sheets in 24 Premier League games this season.
"I think we weren't great in the first half. We conceded another easy goal. I think we have to defend better," said Rodri.
"We knew about their counter-attacks and fast players, but we have to defend the counter-attack better. From there, it's always more difficult to come back."
Mauricio Pochettino's men have often saved their best performances for the biggest challenges during a difficult season for the Blues.
Chelsea took points off all three title contenders at home earlier in the season and finally produced a counter-attacking display on the road that offers Pochettino hope ahead of next weekend's League Cup final against Liverpool.
"I feel like the lads are confident," said Chelsea midfielder Conor Gallagher.
"We have had some good performances, and then today against a top team. I feel like we are going into the next game with a lot of confidence and we are excited for it."
Haaland's night to forget
Chelsea should have led much earlier in the first half as Nicolas Jackson failed to beat Ederson when clean through after a slick counter-attack cut City wide open.
Pep Guardiola's men did not learn their lesson as another ex-City man Cole Palmer sent Jackson in behind and he picked out Sterling, who coolly cut inside Kyle Walker and fired into the far corner on 42 minutes.
Sterling's celebrations were muted, but the goal would have been greeted with glee in Merseyside and north London.
Erling Haaland had headed over City's only clear chance of the opening 45 minutes, but they flew out of the blocks after the break.
Kevin De Bruyne's dipping free-kick landed on the roof of the net before Sterling was exceptionally lucky to avoid conceding a penalty for bringing down Walker inside the area.
However, as City chased an equaliser they became even easier to pick off on the counter.
Ederson produced a stunning save to deny Sterling his second and Ruben Dias needed to head Ben Chilwell's follow-up effort off the line.
Haaland's pace and power finally took him clear of the Chelsea defence 25 minutes from time, but Djordje Petrovic was equal to his deflected effort at the near post.
The Norwegian had nine shots on goal, but his night to forget was then rounded off when he left the 53,000 capacity crowd aghast as he headed well off target with the goal gaping from a perfectly-weighted De Bruyne cross.
City did at least salvage a point as Rodri maintained his own personal year-long unbeaten record.
The last time the Spaniard was on the losing side in a City shirt was February 5, 2022.
The man who scored the winner in last season's Champions League final needed the aid of a deflection as his driven effort flew into the top corner off Trevoh Chalobah.
An unexpected point lifts Chelsea back into the top half of the table and within six points of the top six.
