Sterling has now scored in both of Chelsea's games against Manchester City this season, after also netting in their 4-4 draw at Stamford Bridge in November
City still lost ground in the title race after seeing Liverpool and Arsenal both post emphatic wins earlier on Saturday, but this has to go down as a point gained given how close they came to defeat.
Raheem Sterling gave Chelsea the lead against his old team just before half-time, finishing off a brilliant counter-attack by meeting Nicolas Jackson's cross, cutting inside Kyle Walker and curling his shot home.
The visitors looked threatening on the break all game, with Jackson earlier spurning an even better chance from Malo Gusto's cross when a heavy touch allowed Ederson to smother his shot, and City's keeper also denied Sterling a second from point-blank range.
City were racking up the chances too, but seemed unable to take any of them, or even seriously test Chelsea goalkeeper Djordje Petrovic despite piling on the pressure in the second half.
Erling Haaland was the main culprit, with his worst miss coming when he somehow headed wide from a delicious Kevin de Bruyne cross.
The defending champions were facing their first home league defeat since November 2022, until Rodri struck with seven minutes to go.
After Walker's shot was deflected into his path on the edge of the box, Rodri fired in a ferocious first-time strike that was going in anyway but took a touch off Chelsea substitute Trevoh Chalobah on its way into the net.
The draw sees City drop to third in the table, four points behind leaders Liverpool but with a game in hand - they can close the gap, and leapfrog second-placed Arsenal, if they beat Brentford here on Tuesday.
Chelsea, who were minutes away from a third successive away win, stay 10th, but head to Wembley for next weekend's Carabao Cup final on the back of one of their best displays of an erratic campaign.
-- Courtesy of BBC Sport