Goals from Dickson Etuhu - his first for the club - and Daryl Murphy, who blasted home a 75th-minute piledriver from 25 yards, clinched the points, although the Wearsiders rode their luck at times as the visitors were twice denied by the woodwork.
The win lifted Sunderland into 14th place and to within two points of derby rivals Newcastle, but Keane is in no mood to allow himself to get carried away.
He said: "We have just got to try to keep getting positive results and the table will take care of itself.
"There is no point looking at the table and losing football matches. We have got to put on positive performances.
"Credit to Wigan. As you would expect, it was very hard for us. We rode our luck a little bit, but we maybe earned that little bit of luck. Two good goals, a clean sheet - we are fairly happy. Sometimes, you have got to make your own luck. Yes, we have had setbacks, but that's part of life, that's part of football in particular.
"We have been tested, particularly with injuries in vital areas, but the players showed good character today. If you want to play for this football club, character is most certainly at the top of my list."
Wigan boss Steve Bruce could not quite believe his side had not managed to pick up anything from the game.
He said: "Sometimes the game is cruel. We did enough there, for me, to win the game. I cannot see why the referee gave a foul for the free-kick (for the first goal), and then the second goal is a wonder goal, isn't it?
"You just scratch your head then and think it is not going to be your day. But we missed chance after chance after chance. We didn't score so we go away empty-handed. You scratch your head and wonder why.
"But certainly from what I have seen there today, if we keep playing like that, I am convinced we will be all right. We played with a great spirit and attitude for it and for me, were the better team. But we lost 2-0."