The Brazilian fired a 60th-minute shot that struck the shoulder of Man City defender Vincent Kompany and flew past substitute goalkeeper Kasper Schmeichel as the Tigers ended their run of three league losses.
"It was a fantastic second-half performance by our boys," said Hull manager Phil Brown, whose team has produced stunning victories over Arsenal, Tottenham and West Ham in its first season in the top flight and holds sixth spot.
"I gave them a lot of stick at halftime because of the way we threw a goal lead away."
City, which had also lost three in a row, led through two goals by Stephen Ireland after Daniel Cousin had given Hull the lead.
The first two goals at K.C. Stadium came from awful defensive errors.
City defender Tal Ben Haim's weak pass back toward goalkeeper Joe Hart was intercepted by Cousin, who poked the ball home. Hart went off with a foot injury and was replaced by Schmeichel.
The visitors equalized in the 37th minute from another blunder. Although a move had broken down in the Hull area, Tigers defender Kamil Zayatte, surrounded by three teammates including his goalkeeper, passed the ball straight to Ireland, who had time and space to shoot home.
Ireland made it 2-1 in the 44th with a well-flighted shot from the edge of the area, before Geovanni equalized with a free kick.
"We are disappointed with the second (Hull) goal because we didn't think it was a free kick and they benefited from that," said Man City manager Mark Hughes, whose team climbed three spots to 12th. "It's all about (referees') interpretation. We felt a bit hard done by and maybe similar situations weren't given in our favor."
Ayegbeni Yakubu turned home a free kick for the equalizer in Everton's 1-1 draw with Middlesbrough, but the Toffees fell further off the pace in the race for spots in next season's UEFA Cup.
Boro took a surprising ninth-minute lead at Goodison Park but Everton had chances to win the game and the draw means David Moyes' men fell further behind the leading title contenders, sitting in seventh place with 13 points to make up.
Boro winger Stewart Downing sent a sideways pass to an unmarked Gary O'Neil on the right, and the midfielder fired a lot shot which beat goalkeeper Tim Howard and went in off the inside of the near post.
Yakubu should have leveled in the 14th when he got clear of Boro defender Emanuel Pogatetz. But goalkeeper Ross Turnbull raced off his line to block the shot with his left hand.
Joleon Lescott hit the post with a lob, Phil Jagielka and Tim Cahill both went close with headers before the home side equalized in the 65th minute.
Mikel Arteta fired a free kick in from the left and Yakubu bent his back to deflect the ball home off his shoulder.
"We missed a lot of opportunities and have played better," Moyes said. "When Middlesbrough went ahead with a goal on the counterattack there was always the chance that they could do that again, so we needed to be careful.
"But give us credit, we kept going forward, although we found it very difficult to score."
On Saturday, Chelsea won a record-equaling 10th league away game in a row - 3-0 at last place West Bromwich Albion - to stay ahead of Liverpool on goal difference at the top of the Premier League standings.
Liverpool stayed level on 32 points from 13 games - just over a third of the way through the season - by winning 2-0 at Bolton and Manchester United moved up to third with a 5-0 triumph over Stoke although the Red Devils are still eight points behind the co-leaders with a game in hand.
Arsenal lost 2-0 at home to Aston Villa to slip to fourth and that keeps Martin O'Neill's Villa in fifth.
Harry Redknapp's revival at Tottenham ended with a 2-1 loss at Fulham and Saturday's other results were Blackburn 1, Sunderland 2; Newcastle 2, Wigan 2; West Ham 0, Portsmouth 0.
