Arsenal-bound playmaker Samir Nasri also came on for the final 15 minutes but it changed nothing.
French midfielder Nasri has been out since injuring his hamstring against Huddersfield on 30 January.
Nasri also played a fine one-two with Silva but overhit his pass with Balotelli waiting to pounce.
Nasri has come a long way - on Tuesday he will attempt to show just how far.
BBC: Arsenal star Samir Nasri primed for Barcelona challenge
But having waited 52 years for one goal, City quickly supplied another as Nasri dragged France level again.
"All of these players - Fabregas, Nasri, Messi, Xavi, Andres Iniesta - are all very intelligent, " he added.
BBC: Arsenal star Samir Nasri primed for Barcelona challenge
"It was a combination of touch, intelligence, special talent and calmness as well, " Wenger said of Nasri's goals.
City built a 2-0 lead on goals by Gareth Barry in the third minute and Nasri in the 29th.
They did not have to wait long to get it as Nasri doubled their advantage three minutes after the restart.
Nasri stepped up to score from the spot and another penalty, followed by an Andrey Arshavin goal, wrapped it up.
It was interesting to see Nasri play in central midfield against Middlesbrough on Sunday, because he normally plays on the left.
Tomas Rosicky flashed a shot across goal and Nasri sent a drive just wide as Arsenal picked and probed at Villa.
Nasri then made two crucial contributions at either end of the pitch to ensure Arsenal's safe passage into the last eight.
This reinforces Grimandi's belief that Nasri is starting to warrant mention in the same breath as some of Barcelona's mesmeric stars.
BBC: Arsenal star Samir Nasri primed for Barcelona challenge
Nasri will join a large French contingent at Arsenal which already include captain William Gallas, Gael Clichy, Abou Diaby and Bacary Sagna.
Meanwhile, Samir Nasri and Aaron Ramsey have joined the Gunners, who are now strongly being linked with Aston Villa midfielder Gareth Barry.
Nasri, 23, limped off as he chased a long kick up-field from keeper Manuel Almunia in a game the Gunners won 2-1.
The first glitch in Arsenal's relaxed afternoon occurred when key midfielder Samir Nasri pulled up with a hamstring injury and was replaced.
Ten minutes in, David Silva's defense-splitting through ball found Samir Nasri, who unleashed a shot that left Spurs goalkeeper Brad Friedel no chance.
WSJ: The Magic Behind Manchester City's 3-2 Win Over Tottenham
Samir Nasri rescued a point for France in Donetsk after his Manchester City team-mate Joleon Lescott had fired England into a first-half lead.
Last summer saw Arsenal lose two of their start players, Samir Nasri to rivals Manchester City and club captain Cesc Fabregas to Barcelona.
First-half goals from Samir Nasri and Denilson set the Gunners on their way to the knockout stage for a 10th campaign in succession.
Gael Clichy's cross was headed off target by Nicklas Bendtner, who then failed to get on the end of another dangerous ball from Nasri.
Nasri's cross looked to be posing no serious threat, but a slight touch off Jamie Carragher wrong-footed Johnson, who bundled the ball past Reina.
Arsenal manager Arsene Wenger said that Nasri had "great potential" and could now allow unsettled Belarus international Alexander Hleb to leave the Emirates Stadium.
The hosts were playing their typically free-flowing game and Samir Nasri and skipper Fabregas, back from injury, both wasted good chances inside the box.
They finally ended the siege after 23 minutes when Samir Nasri broke into the area and curled a shot narrowly wide with Valdes struggling.
Wenger also hailed Samir Nasri, who capped an excellent performance with a superb goal, turning three defenders before firing in from an acute angle.
BBC: Nicklas Bendtner delights Arsenal manager Arsene Wenger
Nasri's 25-yard shot against the woodwork turned out to be their best effort, but the league leaders were largely subdued on a freezing night.
Fulham boss Mark Hughes admitted Nasri had been the difference between the sides, but said he was proud of how his team had played.
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