Kieran Richardson opened his Sunderland account just 13 minutes into his first start since August, and then fired in the corner which allowed Kenwyne Jones to stretch the lead with a powerful 32nd-minute header.
However, Wanderers grabbed a lifeline four minutes before the break when El-Hadji Diouf drifted a free-kick inside the far post, and despite a late assault, the home side held out.
Keane was delighted after a tense finish in which substitute Daryl Murphy eased the nerves at the death.
He said: "It's nice, it's nice to win. It seems like a while since we have won.
"It wasn't too pretty, but it's a win and the players deserved it.
"We have played a lot better this year and not got a result, but today we just about ground out a good one."
Keane had admitted in the run up to the game that it was a must-win encounter, but said afterwards: "I say that every week.
"We try to approach every game (the same) - put it this way, what other way would you approach a game? Must lose? Must draw?
"You must win, that's what you are in the game for."