Tevez seized on a hopeless back-header by Mohamed Diame to nip in and score City's opener at the end of the first half then set up the simplest of second goals for Yaya Toure as City coasted home.
Mancini believes his decision to award the Argentinian the club captaincy will continue to do wonders for his form and also insists getting back on the scoresheet will lift some of the pressure on the 26-year-old.
Mancini said: "I thought about it [the captaincy] during the summer and I spoke to Carlos about it. He is an important player and he can improve as captain and we can have more of him.
"I'm very happy for him because at this moment he probably isn't at 100 per cent of his form. Maybe his goal today can help him and it is fantastic that he got it today."
Despite two chances for Tevez, City had failed to trouble Wigan keeper Ali Al-Habsi until the defensive error which saw Diame nod back a long Joe Hart goal-kick and allow the striker in to loft the opener into the net.
It was a blow for Wigan who had matched City in most departments up to that point but after the break City came close to adding a second when Tevez mis-kicked a David Silva cross then Pablo Zabaleta brought a save out of Al-Habsi.
City grabbed their second in the 68th minute and again there was an element of fortune about it as Maynor Figueroa's loose header let in Tevez, who swung in a cross which Toure converted.
Wigan's mistakes infuriated boss Roberto Martinez, who said: "We created Manchester City's best chances and that is very disappointing. In any performance the hardest thing should be to concede a goal.
"At the moment from time to time we come out with this softness in our defensive play which really lets ourselves down and puts games out of our reach."