City dominated the early stages of the game and deservedly took the lead after Sterling scored with a curling shot after 17 minutes.
Leeds fought back and almost levelled before the break but Ederson denied Luke Ayling.
Rodrigo was brought after half time and made it 1-1 after 57 minutes when Ederson's failed punch landed at his feet to score.
The goal was Rodrigo's second Premier League goal and first since January 2011 when he scored for Bolton Wanderers while on loan -- nine years and 272 days ago. It is the second longest gap between a player's first two goals in the competition.
The goalkeeper made up for the mistake with a brilliant save from Rodrigo moments later while Illan Meslier denied Sterling at the other end.
"That was good, huh?," Guardiola said. "When both teams want to attack, it's a good game. We made an incredible first 30 minutes when we could have scored the goals we needed.
"It's not easy to play against them. They've showed how good they are."
The result leaves Leeds in fifth place on seven points from four games ahead of City in 10th with four points from three matches.
"It would not have been fair if we won this game," Bielsa said. "It was possible to win the game but it would not have been fair.
"We had to put in an immense physical effort to be on even terms with City. We played our part for the game to be a beautiful one."