Morten Gamst Pedersen struck first when he fired home a 58th-minute free-kick and Jason Roberts added a cool second eight minutes. Charles N'Zogbia reduced the deficit late on.
"We scored two outstanding goals today which made the difference between us and Wigan," said Allardyce.
Allardyce reserved particular praise for substitute Roberts, who missed a golden chance against champions Chelsea last week but rebounded today with his nerveless 67th-minute finish.
"Jason's never let us down at all ever since I've been here," he added.
"While he was disappointed about the chance he missed last week, he gave us a very good performance. And again today he's not only had a good performance but he's scored the winning goal, which is what we want."