Dzeko has scored 20 goals in all competitions this season, the first time he has achieved such a feat in any of his four campaigns at the Etihad Stadium.
The Bosnia-Herzegovina international found the net twice in City's 3-0 derby success at Manchester United late last month, and Begiristain believes that manager Pellegrini has had a huge influence on the 28-year-old.
"I came here one year and three months ago, and I am seeing a different player (in Dzeko)," Begiristain is quoted as saying in the British media.
"And I have to say that the talent was there, all the qualities were there, but now he has the confidence from the manager."
Earlier this season former Barcelona director Begiristain credited ex-Malaga and Real Madrid boss Pellegrini with improving the mood in the City camp.
City were eliminated in the last 16 of the UEFA Champions League by Barcelona but are very much in contention for the Premier League title, trailing leaders Liverpool by four points with two games in hand on the Merseyside club.
And Begiristain has no doubt that the Chilean will help City challenge for European honours in future.
"He likes to play attractively, he likes brilliant football," Begiristain added.
"He's calm. His behaviour has always been an example for the rest of the managers, and I would say that we want to play good football, but we also want to be happy.
"We want to compete for trophies. You know that one year you will win the Premier League and, not in the short term, we will fight for the Champions League.
"The aim is to build a team, to have an idea what kind of football you want.
"Then I know there are some managers in the world that can apply this kind of football, with this philosophy, and then to have the right players."
