The Milan manager praised his players' discipline and determination but stressed that a top-four finish remains the club's main objective.

The derby was decided in the 35th minute when Pervis Estupinan produced a composed finish to give Milan a priceless lead. Timing his run perfectly, the defender met a well-weighted pass into space and fired home from close range, sending the home supporters into celebration.

"It is the most important goal of my life, really," Estupinan said after the match. "It was an enormous effort from everyone."

Inter were hampered by key absences in attack. Marcus Thuram missed the match through illness, while captain Lautaro Martinez remained on the bench as he continued recovering from a muscle injury. Despite enjoying more possession after the break, the league leaders struggled to create clear chances.

Veteran midfielder Luka Modric praised Milan's defensive organisation and first-half display.

"Great performance in the first half," Modric said. "Inter pushed after the restart because they are a strong side, but they created practically nothing against us."

The victory meant Milan completed a league double over their city rivals, having also won the reverse fixture by the same 1-0 scoreline earlier in the season.

Allegri, however, quickly moved to calm growing excitement among supporters dreaming of a late title push.

"We defended in an orderly way and had a few favourable situations," Allegri said. "That said, Inter clearly remain the favourites for the championship.

"Seven points is a big advantage. They are still the strongest team and the clear favourites. We could have been sharper in the final third in some situations."

He added: "We worked for seven months to make sure we reached March in the best possible condition, because this is when the most important games of the season are played and everything is decided."

Milan controlled much of the second half as they searched for a decisive second goal, while Inter lacked their usual sharpness in the final third.

Tempers rose late on when an Inter corner found the net moments after the referee had blown for a foul, forcing a retake that came to nothing. Home fans whistled loudly as tension filled the stadium before the final whistle confirmed a vital derby triumph.

With ten matches remaining, Inter stay top of Serie A on 67 points, seven clear of Milan, but this result ensured the pressure remains firmly on the league leaders as the title race enters its decisive phase.