Having registered just one point and one goal from their opening three league fixtures, Allardyce's team finally started converting possession into goals on Saturday as strikes from El-Hadji Diouf, Jason Roberts and David Dunn wrapped up a 3-1 win.
The manager had already been pleased with his team's level of performance, and now with a first win secured, hopes to see them go on an unbeaten run.
"We'll probably look at the statistics on Monday and see that we've had 20 attempts at Wolves' goal, but this time we've got the right ratio of finishes, we've got three goals," Allardyce told the club's official website.
"Before that we were getting no goals, I hope the turning of the corner gives everybody the boost of confidence they need.
"We are on our way now and I hope we can go on an undefeated run and pick up more wins along the way. We've a difficult game next week against Everton but with a good week on the training pitch we can try and go and get a result at Goodison Park."