The Brazilian is making the most of his extended run in the team in the absence of the injured Sergio Aguero.
But prior to a double in another 4-1 City win at Burnley last week, Jesus had gone 10 games for club and country without a goal.
“I have to do my job, my job is to score goals and help the team,” he told BT Sports.
“Last month I was not scoring so I felt so bad because I have to score, help my teammates. Now the goals are coming, so I am so happy. I cannot stop.”
Dinamo needed to win to have any chance of joining Group C winners City in the last 16 and got off to the perfect start through Dani Olmo’s sweetly struck volley 10 minutes in.
However, even a much-changed City side had way too much quality for the hosts and a trio of fine finishes from Jesus in a 20-minute spell either side of half-time turned the game around before Phil Foden added a late fourth.
Defeat means Dinamo bow out of European competition by slipping to the bottom of the group as Champions League debutants Atalanta finish second behind City.
“We played 75 minutes very, very well,” said City boss Pep Guardiola. “We’d qualified, but we came here for the club, for the prestige, to learn to play in this competition.
“We had many absences, but we got a good result and hopefully it will help us in the future.”
Guardiola made eight changes from the side beaten 2-1 at home by Manchester United on Saturday to leave the English champions 14 points off the top of the Premier League table with Raheem Sterling and Kevin De Bruyne among those left on the bench.
Derby defeat meant City had won just two of their previous seven games in all competitions and another poor night beckoned when Damian Kadzior’s cross was brilliantly smashed past Claudio Bravo by Olmo, despite the Chilean goalkeeper getting a hand to it.
City have now kept just one clean sheet in 12 games, but instead of exploiting the weaknesses in the visitors’ defence, Zagreb sat on their lead and were punished as Guardiola’s men took control of the game.
– Marauding Mendy –
City’s pressure told with an equaliser 11 minutes ahead of half-time.
Dinamo were unhappy play was not stopped as they had a man down injured, but City were within their rights to play on and Jesus rose highest to head home Riyad Mahrez’s cross.
Benjamin Mendy has struggled for fitness and form on his return from nearly two full seasons out injured, but the French left-back’s performance was among the most encouraging of the night for Guardiola.
Mendy made his name rampaging forward for the Monaco side that reached the semi-finals of the Champions League three seasons ago and looked more like his old self as he was involved in both Jesus’s goals inside the first 10 minutes of the second half.
Firstly, neat interplay from Mendy and Foden freed the Brazilian inside the area and he turned onto his right foot before finding the far corner.
Foden was also involved for the third as his pass fed Mendy, whose teasing cross left Jesus with the simple task of prodding into an empty net.
And Foden rounded off a great night for his case for more Premier League playing time by slotting home Bernardo Silva’s cross six minutes from time.
