Ngandu Kasongo and Given Singuluma both scored twice in Lubumbashi as Mazembe delighted their home fans.
Alain Kaluytika scored the other in a one-sided win that put Mazembe in an almost unassailable position for the second leg in Tunis on November 13.
Mazembe, who needed the away goals rule to win last year's Champions League, benefited from the sending-off midway through the first half of Esperance defender Mohamed Ben Mansour.
Yet by then they had the lead courtesy of Kasongo's 19th-minute opener.
There was controversy as Esperance protested that the ball had not crossed the line when Kasongo rose to head home a free-kick.
Kaluytika converted a penalty on the stroke of half-time after being brought down in the Esperance area, before Singuluma snatched both his goals in a four-minute spell after the interval.
Singuluma's first came with a 55th-minute header and his second in the 59th minute from a low shot.
Kasongo completed the scoring with 15 minutes left.
Mazembe's triumph last year came four decades after their success in the competition in 1967 and 1968.
In 1968 Mazembe beat Etoile Filante of Togo 5-0 in the first leg of the final and went on to win 9-1 on aggregate.
