The 21-year-old was the dominant figure in a 4-1 win over Monza, using his 191cm frame to hold off tight marking from the Monza defence throughout, with his work with his back to goal a constant thread through Inter's best moments.
He was involved in every one of Inter's goals bar Yann Bisseck's second, working the ball to Amadou Diouf for the assist that led to Hakan Çalhanoğlu's opener, acting as a link for Yann Bisseck's finish to make it 4-1, and finishing off a flicked backheel of his own to beat marker Lorenzo Lucchesi and goalkeeper Semuel Pizzignacco.
With Lautaro Martínez still working his way back to full fitness and Marcus Thuram starting from the bench, Esposito's display was enough on its own to carry Inter's attack, raising the question of whether the presumed starting strike pairing will hold once the Argentina captain and the Frenchman return to full sharpness.
Last season Esposito scored 10 goals in 48 appearances across all competitions, 22 of them as a starter — numbers he looks well placed to surpass this time around.
Speaking after full time, Esposito played down the idea of setting himself individual targets.
"Objective? The only one I set myself is to improve every year, both in terms of statistics and as an athlete. I wouldn't want to put a number on it.
"Regardless of the contract, I always want to give my best and try to do well."
On that contract situation, Esposito confirmed an announcement is close, with an extension through 2031 expected to be finalised imminently, tying the forward to Inter for the long term after a breakthrough campaign that has already made him one of the most sought-after young strikers in Serie A.