The Lubumbashi 'Ravens' needed the help of an own-goal to hold Saint George in Ethiopia and were well beaten by Wydad Casablanca in Morocco in CAF Champions League qualifiers.
Mazembe, the equal second most successful CAF club with nine titles, gave their best African display this season to beat visiting Medeama of Ghana 3-1 as the group stage kicked off.
Supporters hope this improvement will continue with a victory at the national stadium in Dar es Salaam that would confirm Mazembe as favourites to top Group A.
Ghana-born winger Solomon Asante believes Mazembe can atone for finishing Confederation Cup runners-up in 2013 by winning the competition this year.
"We are determined to make up for our failure to lift the trophy a few years ago," he told the Congolese media.
"Defeating Medeama marked a change in our fortunes after the disappointment of failing to defend the Champions League title.
"Mazembe have good footballers who are determined and my hunch is that we are going to go all the way this season and lift the Confederation Cup."
Young Africans' Dutch coach Hans van Pluijm believes extensive training in Turkey before and after a 1-0 matchday 1 loss to Mouloudia Bejaia in Algeria will benefit his team.
"Training in Turkey was very fruitful. We enjoyed excellent facilities so morale is high and the players are determined to succeed.
"Mazembe are a strong side, but we are good enough to challenge them. A key factor could be our supporters -- I hope they come to the stadium in large numbers."
Medeama have cause for optimism when they host Bejaia in Sekondi Wednesday having won all three previous home matches in the Confederation Cup this year by 2-0 scorelines.
The Group B highlight comes Wednesday when title-holders Etoile Sahel of Tunisia host shock 2010 Confederation Cup winners FUS Rabat of Morocco.
Etoile began with a 2-1 away loss at another Moroccan outfit, Kawkab Marrakech, while FUS won 1-0 at home against Al Ahly Tripoli of Libya.
Ahly, handicapped by having to stage home fixtures in Tunisia owing to security concerns, meet Tuesday a Kawkab team without a win in four 2016 CAF away matches.