Stefano Pioli's side jumped ahead of Inter Milan and Napoli, who drew 1-1 in Naples on Saturday, to go top with 55 points.
It completed a superb week for Milan, in which they defeated rivals Inter in the Milan derby and hammered Lazio 4-0 in the Coppa Italia quarter-finals, leaving Inter one point behind with a game in hand and Napoli two points back in third place.
"We can call it a perfect week because you can't do better than this," Milan midfielder Sandro Tonali told DAZN.
"We are proud and satisfied but we won't rest on our laurels because that would be stupid. We need to reset everything and continue along this path."
Portugal international Leao skipped past his marker and found the bottom corner from a tight angle after eight minutes to notch up his 10th goal of the season in all competitions.
Sampdoria goalkeeper Wladimiro Falcone kept his side in it with a string of fine stops, but it was not a happy return to Milan for Samp coach and former Rossoneri boss Marco Giampaolo, whose side remained 16th with 23 points.
Pioli praised his side's improved maturity ahead of the one-year anniversary of a shock defeat to Spezia that saw their 2020-21 title bid crumble, and his players did not let him down.
Milan knew that three points would send them top as they look for a first Serie A title since 2010-11, and they did not take long to go in front.
Goalkeeper Mike Maignan launched a long ball out to the wing, where Leao controlled it, cut inside a defender and calmly finished.
The Frenchman was denied again with a header that was tipped over the bar, while Ante Rebic's shot was beaten away by the impressive 26-year-old.