Sergio Aguero was also on target in the 4-3 win, while Carlos Tevez was left warming the bench but could come back into contention for the visit of Stoke on New Year's Day.
Mancini believes the ability to tweak a potent frontline will be key if his men are to claw back a seven-point gap to rivals Manchester United.
"We changed against Norwich because we played three games in six days and needed to have fresh players, but we are sure that all of our strikers can start to score like they did here," Mancini said.
"We have won games with Carlos and Aguero, Edin and Carlos, Aguero and Edin; all these three players, if they work hard like this, they can score important goals for the season."
But Dzeko, most often used as an impact player from the bench, remains coy over his future.
"The manager gave me the chance to play and I think I paid him back," he said. "We will see what the future brings."