De Canio was called back to his native Italy by a family bereavement, leaving performance manager Joe Dunbar in charge.
Rangers, who moved six points clear of the Championship relegation zone after this victory, were superb with Akos Buzsaky's third goal adding gloss to the scoreline.
Rangers included six January transfer window signings in their side, while there was just the one change to the City team that beat Blackpool last week with Dele Adebola, signed from Coventry on deadline day, starting up front.
The hosts started the brighter and on 18 minutes Agyemang made it four goals in his last four games by smashing into the far corner after Rowan Vine's clever diagonal pass had put him beyond the Bristol City defence.
Rangers were easily on top and Johnson was so incensed by his side's display that, in a break in play for an injury, he called all of his outfield players together on the side of the pitch and read them the riot act.
It made little difference as Agyemang then combined nicely with Vine to lay the ball off to Buzsaky.
The Hungarian's shot was deflected but fell perfectly for the Ghanaian, who could barely miss from three yards.
The hosts scored a deserved third goal on 62 minutes after another fine passing move.
Buzsaky was the scorer as the former Plymouth man showed impressive technique to volley home with the aid of a slight deflection from 20 yards after Agyemang had laid the ball back into his path.
It became clear it was not going to be City's day as Adebola fired against the far post and, when the ball came back to him, he saw his first-time effort hit Lee Camp and bounce away to safety.
Rangers played out the last 20 minutes with ease as they paid tribute to their absent manager in the best possible way.