Nolan sealed the victory with his 100th career goal but Allardyce was full of praise for a defensive effort which kept Wigan at bay.
"I am pleased for Kevin. It must have played on his mind that he was on 99 goals because has waited so long to get his 100 and now he has got it with great technique," Allardyce said.
"When we didn't have the ball, which was for long periods, we were excellent in our defending today. We were very resilient and dogged.
"There is no doubt that if you can win a game in the Barclays Premier League when not playing your best, it shows a measure of your determination.
"Rather than surrender, we stayed in the game until we got a chance to clinically finish them off which is what we did."