Ki-Hyeon Seol and Danny Murphy combined as the former Spurs man rolled the ball past goalkeeper Kasper Schmeichel in the 75th minute.
This six-goal bonanza put paid to Sven-Goran Eriksson's conservative start to his Premier League campaign - City's previous five games had ended 1-0.
City held on for the draw - their first of the season - and Sanchez managed to break the hoodoo of conceding late as Fulham, urged on by an expectant crowd, showed great character.
After a slow start, the game really ignited after the interval.
The teams went into the break with one goal a piece, with Welshman Simon Davies having opened the scoring for the home side.
After 13 minutes the tousle-haired winger ghosted in from the right, undetected by City's sluggish defence, and ran in between Micah Richards and Richard Dunne to nod home Hameur Bouazza's cross at the near post.
The City skipper, making his 250th Premier League appearance, was culpable after ball watching, but his team managed to equalise through left-winger Martin Petrov ten minutes before the break.
The Bulgarian cut inside from the left and breezed passed the woeful challenges of Aaron Hughes and Chris Baird before shooting.
Fulham keeper Antti Niemi should have done better, though Petrov did not mind - it was his first for City since signing from Atletico Madrid in the summer.
The goal spurred City on and Fulham played as though they were expecting to lose, though Sanchez had other ideas.
At half-time he brought on striker Diomansy Kamara, who made an immediate impact.
He was felled on the left edge of the area by Dunne and Bouazza netted the resulting free-kick.
Petrov, galvanised by his first-half goal, began to look menacing, and his shot three minutes later was parried by Niemi, but only as far as Emile Mpenza, who
obligingly nodded in.
The winger then put City ahead ten minutes later after volleying home a one-two with Elano.
Murphy and Seol came on with 22 minutes left and Fulham looked hungry again.
Murphy's goal - his first for the club - was deserved for Fulham's tenacity.
The 30-year-old could have won the game for Sanchez but he blazed over two minutes later.
In the end a draw was a fair result in a game where both teams tried their hardest and produced a great spectacle.