Milan, who are reported to be sold to Bahrain based investment firm Investcorp, reclaimed the summit after briefly being bumped down to second before kick-off in front of over 70,000 fans at the San Siro.
But Leao's cushioned 11th-minute volley from Pierre Kalulu's cross and a Junior Messias strike with three minutes remaining were enough for Stefano Pioli's side to maintain their two-point lead over local rivals Inter.
Attention will now turn to third-placed Napoli who face in-form Roma on Monday evening hoping to move level on 69 points with Inter, while Juventus sit nine points off the pace ahead of their home fixture with Bologna on Saturday.
"The more games we play, the more important each match becomes," said Messias.
"We knew today wouldn't be easy but we were good and we got the three points that make us want to keep fighting."
Portugal forward Leao's sumptuous finish was the highlight of an otherwise uninspiring display which showed why Milan have struggled to put away Serie A's lesser lights since the turn of the year.
Milan kept their seventh straight clean sheet in all competitions – having lost right-back, Davide Calabria, to a stomach bug shortly before kick-off – but it was a night of few chances for the seven-time European champions.
Olivier Giroud's miscued overhead kick in the 57th minute was the first truly good opportunity after Leao's opener.
Leao then went close to doubling the hosts' lead when he forced a good save from Salvatore Sirigu, but Messias put the home crowd into a party mood when he smashed in the second after being denied by Italy international in the Genoa goal.
"We have to make the pressure feel like nothing more than positive energy because we are challenging for something that when we started working together was unthinkable," said Pioli
Milan now face Inter in the second leg of their Italian Cup semifinal on Tuesday before travelling to Rome to face Lazio next weekend as takeover talk hots up.
Neither Milan nor Investcorp has said anything about the club for sale to American investment fund Elliott for around one billion euros ($1.08 billion).
Elliott took control of the club in 2018 when the previous owner Li Yonghong defaulted on a loan taken out to finance the 740 million-euro purchase of Milan from former Italian prime minister Silvio Berlusconi.