Defeat for the Lubumbashi side would have left them unable to make it through to the last four, but they kept the group wide open with a scintillating display.
Enyimba were missing several key players, including top-scorer Stephen Worgu, but TP Mazembe were always in control.
Nvete Luyeye opened the scoring for the home side with 18 minutes played, and it was 1-0 at half-time - thanks to some strong defending by Enyimba.
But mid-way through the second-half Enyimba handled in the area and Mputu Mabi stepped up to convert the resultant penalty.
The match was all over as a contest when, with 11 minutes to go, Patou Kabangu drove home the third for TP Mazembe.
In the other match in Group B, Coton Sport of Cameroon scored a narrow 1-0 win over visiting Al Hilal.
Baba Ousmaila got the only goal of the game and Hilal had Alaeldin Gibril sent off midway through the second half.