The Brazilian forward, a second-half sub for compatriot Elano, chested down a pinpoint ball from Didi Hamann to go through on goal but he took his shot too early and blazed over the crossbar.
But Geovanni made amends right at the death, nodding down for Stephen Ireland to unleash an exquisite volley on the run which rocketed into the top corner.
"I was sitting on the bench and everyone thought that when Geovanni didn't take that chance then it's a draw and that's it," said Sven.
"But we had one more chance and what a goal from Stephen Ireland. He took it absolutely fantastically."
City took an 11th-minute lead through Martin Petrov following a goalmouth scramble which saw Elano hit a post and Emile Mpenza have a shot saved.
The Blues failed to build on that early lead, though, and Reading's James Harper equalised with a sweet strike in the 43rd-minute.
Moments later City's Croatia international Vedran Corluka went off for Sun Jihai with what looked like a hamstring injury, but City regrouped and eventually made the breakthrough, making it 8 wins from 8 at home with virtually the last kick of the game.
"I think we started the game very well and got 1-0 in front," Sven added. "Then together with injuries and one thing and another, we lost the rhythm and our way a bit. We let Reading into it and they scored.
"The spirit saw us through and we worked hard to win the game and create chances. We were lucky that we took one of them and won the game."