Leao struck twice in each half for the champions in a pulsating clash at the San Siro which put Milan a point ahead of Atalanta and Roma at the summit.
Fans bounced in the stands after a thrilling match full of goalmouth incidents which were decided by Leao and Olivier Giroud, who after Marcel Brozovic's 21st-minute opener for Inter shot Milan two goals to the good on the hour mark.
However, they also had the magnificent Mike Maignan to thank for the three points after the France goalkeeper pulled off four superb stops from Lautaro Martinez, Edin Dzeko – also a scorer – and Hakan Calhanoglu.
A second defeat in five matches leaves Inter fifth, level on nine points with Juventus who underwhelmed in their 1-1 draw at Fiorentina, the first of three matches on a bumper Saturday which finishes with Lazio hosting Liverpool's midweek opponents Napoli.
An already breathless encounter which started with the usual spectacular pre-match displays from the fans kicked into an even higher gear in the second half.
Giroud put Milan head in the 54th minute in fortunate fashion when he met the irrepressible Leao's low cross with a scuffed finish which squeaked past Samir Handanovic.
Leao then nearly brought the house down six minutes later, a jinking run leaving him in front of Handanovic just yards from goal where he made no mistake.
Substitute Dzeko pulled a goal back seven minutes later and then Maignan stepped in to keep resurgent Inter out and ensure Milan claimed local bragging rights and top spot.