A Samuel Eto'o brace helped Inter to a 3-2 Coppa Italia victory over Genoa, but Andrea Ranocchia gave away a penalty on his full debut.
Leonardo hoped to maintain his 100 per cent record at the helm as the Nerazzurri began their defence of the trophy.
Ranocchia was given his full Inter debut against the team he left only last week. He immediately had a tough test, having to shrug off Gergely Rudolf in the box to stop a dangerous counter-attack.
Inter broke through with their first genuine scoring opportunity after 15 minutes. Eto'o trapped a Sulley Muntari cross from the left and squeezed between Domenico Criscito and Emiliano Moretti as if they weren't even there, coolly prodding past the goalkeeper.
It was almost 2-0, but Alessio Scarpi beat away another Eto'o strike, while Genoa threatened on the counter following a MacDonald Mariga error.
Just before the break, Muntari unleashed a screamer from distance that took a coat of paint off the upright.
Moments later Inter did get their second with Eto'o again. It was a well-worked move, as Douglas Maicon crossed low from the right, he controlled with one touch to leave his marker stranded and smashed the angled drive in at the near post.
After the restart Luca Castellazzi needed to be alert as his palms were stung by a sudden Richmond Boakye snapshot.
However, it was a disaster full debut for Ranocchia, who brought down his former teammate Rudolf for a penalty. Houssine Kharja sent Castellazzi the wrong way to get Genoa back into the game.
Moments later Marco Materazzi gave the ball away in the final third, but Boakye's shot was charged down.
However, the Nerazzurri restored their two-goal cushion with Mariga's powerful header from a Maicon corner.
New Genoa signing Juraj Kucka blasted just over from distance, Castellazzi smothered a Giandomenico Mesto solo effort and Criscito strike, while Giuseppe Sculli was halted for a dubious offside flag.
At the 87th minute, Castellazzi needed a fingertip save to take Criscito's attempt out of the near top corner, then was at full stretch to turn Dario Dainelli's daisy-cutter round the post. Inter visibly relaxed in the final half-hour and allowed Genoa to run at them comfortably.
The pressure eventually paid off with a consolation goal, as Miguel Veloso whipped in a free kick for Sculli's header. It was a special goal for Sculli, who was hours away from joining Inter in the summer before the club changed its mind.
Inter squeezed through and will face the winners of Napoli-Bologna in the quarter-final.
Inter 3-2 Genoa
Scorers: Eto'o 15, 43 (I), Kharja pen 54 (G), Mariga 60 (I), Sculli 90 (G)
Inter: Castellazzi; Maicon (Rivas 88), Ranocchia, Materazzi, Santon; Zanetti, Cambiasso, Mariga; Muntari (Biabiany 57); Pandev, Eto'o (Obi 70)
Genoa: Scarpi; Rudolf (Sculli 62), Dainelli, Moretti, Criscito; Kucka, Veloso, Kharja (Palacio 62); Rafinha; Jelenic (Mesto 46), Boakye
Betting on Serie A? Bet365 are offering a 100% deposit bonus, up to £200 - find out more