Morten Gamst Pedersen swung home a 58th-minute free-kick and Jason Roberts added a cool second eight minutes later before Charles N'Zogbia reduced the deficit late on.
Coming after last week's fine but ultimately fruitless performance against Chelsea, Allardyce admitted: "We've got a reverse scenario today where we haven't played as well as normal but we've got a win.
"The difference between Chelsea and us last week was their quality for their two goals and we scored two outstanding goals which made the difference between us and Wigan."
Allardyce reserved particular praise for substitute Roberts, who missed a golden chance against the champions last week but rebounded today with his nerveless 67th-minute finish.
Allardyce added: "Jason's never let us down at all ever since I've been here. While he was disappointed about the chance he missed last week, he gave us a very good performance.
"And again he's not only had a good performance but he's scored the winning goal, which is what we want."
Allardyce dismissed suggestions Pedersen's opener had a touch of good fortune about it after the Norwegian's free-kick from the right touchline eluded everybody and curled into the top corner.
Allardyce added: "There was nothing fortuitous about it. He does it every day in training and that's why you put a left-footer down the right flank."
Wigan boss Roberto Martinez criticised referee Kevin Friend for disallowing a first-half effort from N'Zogbia, apparently due to a foul on Pedersen in the box.
N'Zogbia played a superb one-two with Hugo Rodallega and burst into the area, where he squeezed between Pedersen and Michel Salgado before poking home.
Martinez said: "I don't know what was wrong with N'Zogbia's goal. Football is a game of contact and certainly when you come to Ewood Park there's a physical side to the game.
"I know the referee has got a very difficult job but that decision really cost us.
"If you look at the replay he (the referee) is in a good position so he must be guessing what happened.
"It was a low point for us and it was mentally hard to recover from that. In the second half we started well but two quick goals out of nothing leaves you feeling a little bit hard done by."
However, Martinez said he could take some positives out of the game after his side showed plenty of improvement after their dismal display at Fulham last week.
"I'm pleased with the reaction," he added. "We controlled the game and took risks and created a couple of good chances. We showed character to get a goal back but it was just one of those days."