With Sergio Aguero still injured, the spotlight remains on City’s other forwards and Bony set them on the way to a comfortable win at the Etihad Stadium with a fine header.
The lively 19-year-old Iheanacho then got in on the act after Kevin De Bruynehad maintained his recent scoring streak with City’s second.
Yaya Toure added a fourth from the penalty spot and substitute Manu Garcia rounded off a good night’s work with a fifth in stoppage time after a Damien Delaney consolation.
City’s victory came without them ever really hitting top gear, although they were soon into their stride as De Bruyne seized on a Scott Dann mistake and burst clear only to shoot across goal after two minutes.
Palace threatened briefly as Yannick Bolasie sliced a volley wide and then both he and Joe Ledley had chances in a goalmouth scramble but Willy Caballero eventually dived on the ball.
Pablo Zabaleta and Bolasie had a bruising battle on the flank and both required lengthy treatment after a clash of heads. Zabaleta was bandaged in now trademark fashion while Bolasie was down for some time – accounting for most of the five minutes first-half stoppage time – before eventually getting back to his feet.
Worse did follow for Zabaleta as he was carried off on a stretcher after a clash with Wilfried Zaha early in the second half, but by then City were already 3-0 up and cruising.
Their opening goal came in the 22nd minute as Bony met a De Bruyne corner with a firm header that Wayne Hennessey could not keep out.
It was a fine finish and seemingly just the confidence boost the Ivorian needed as he continues to lead the line with Aguero out, but he could not follow it up.
With his next chance he sliced high and wide, and he could then only shoot tamely at Hennessey. There was an even poorer effort after the break as he completely miskicked in front of goal.
City doubled the lead just before the interval as Iheanacho raced onto aFernando pass and pulled the ball back for De Bruyne to tuck in from close range.
Palace should have pulled one back immediately but Ledley blasted over after a cross squirmed out of Caballero’s grasp.
City upped the tempo to claim a third just before the hour. De Bruyne, who had himself tested Hennessey just moments earlier, squared for Iheanacho to bury a low shot.
Palace’s misfortune continued as Zaha slipped when in on goal and Patrick Bamford could not beat Caballero. They then needlessly conceded a penalty as Damien Delaney bundled over Mangala at a corner. Toure confidently converted from the spot.
Delaney pulled one back with a superb header with 89 minutes on the clock but 17-year-old Garcia, having been introduced as a late substitute, showed fine composure to claim City’s fifth.