After warning shots from Jesus Navas and Fernandinho, City went ahead in the 51st minute.
De Bruyne brought down a bouncing ball just inside the Arsenal half and held off Hector Bellerin before surging towards goal, cutting inside Elneny and guiding a low shot past Cech’s outstretched right hand.
But the introduction of Theo Walcott for Iwobi provided an injection of dynamism to Arsenal’s attack and after he had lofted a shot wide from Giroud’s lay-off, the visitors equalised through Sanchez.
Picking the ball up deep, the Chilean forward rolled a pass forward to Giroud, who brilliantly steered it back into his path, and Sanchez powered through a gaping hole in the City defence to clip a shot past Hart.
Pellegrini sent for the cavalry, with Raheem Sterling, Yaya Toure and Wilfried Bony all joining the fray, but the closest his side came to a winner was a deft Bony volley that crashed against the bar.
Pellegrini, who bows out at Swansea City next Sunday, covered his face with his hands in anguish.
Euro blow for England as Welbeck injured
Arsenal striker Danny Welbeck was forced off with an apparent knee injury during the first half of his side’s Premier League game at Manchester City on Sunday.
The England international seemed to hurt his right knee in a challenge with Bacary Sagna and after receiving treatment he tried to play on, only to walk straight off the pitch and down the tunnel moments later.
It could be bad news for England manager Roy Hodgson, who announces his squad for the European Championship on Thursday.
Welbeck, 25, spent the first six months of the season on the sidelines after undergoing surgery on his left knee in September.
In better news for Hodgson, and Arsenal manager Arsene Wenger, Welbeck’s replacement was Jack Wilshere, who returned to action last month after eight months out with a fractured shin.
The score was 1-1 when Wilshere came on in the 24th minute, with Olivier Giroud having cancelled out Sergio Aguero’s eighth-minute opener for City.
Arsenal were already missing German playmaker Mesut Ozil due to what the club said was a “slight hip injury”.
Collated English Premier League results on Sunday:
Liverpool 2 (Allen 35, Firmino 76) Watford 0
Manchester City 2 (Aguero 8, De Bruyne 51) Arsenal 2 (Giroud 10, Sanchez 68)
Tottenham 1 (Son 16) Southampton 2 (Davis 31, 72)
Played Saturday
Aston Villa 0 Newcastle 0
Bournemouth 1 (Ritchie 82) West Brom 1 (Rondon 16)
Crystal Palace 2 (Gayle 47, 68) Stoke 1 (Adam 26)
Leicester 3 (Vardy 5, 65-pen, King 33) Everton 1 (Mirallas 88)
Norwich 0 Manchester United 1 (Mata 72)
Sunderland 3 (Khazri 41, Borini 67, Defoe 70) Chelsea 2 (Costa 14, Matic 45+3)
West Ham 1 (Kingsley 69-og) Swansea 4 (Routledge 25, Ayew 31, Ki 51, Gomis 90+3)