After a 2-2 first-leg draw in Paris last week, the tie remained in the balance in Manchester thanks to Sergio Aguero’s missed penalty for City in the first half.
The home side had Joe Hart to thank for three fine saves at 0-0, notably a ferocious Zlatan Ibrahimovic free-kick that the England goalkeeper clawed to safety.
But, roared on by a capacity crowd of 53,039 that supplied an unforgettable atmosphere, City held their nerve at the back before De Bruyne’s decisive strike 15 minutes from time with their only shot on target.
The final whistle brought scenes of pure emotion from the fans at Etihad Stadium, who were already in uncharted territory.
England’s last remaining representatives in Europe’s elite club competition had never reached the quarter-finals before this season – now they can dream of the final in Milan.
First they can look forward to Friday’s semi-final draw, after winning what was viewed as the battle of Europe’s richest clubs with a PSG side who have now fallen at the last-eight stage for four successive seasons.