Walcott was introduced just after the hour mark, and it proved a key substitution as the pace of the England Under-21 winger helped stretch the Bolton defence.
Kolo Toure drilled in a 25-yard strike to open the scoring after 68 minutes, with substitute Tomas Rosicky wrapping up the points with a close-range effort after Walcott had gone on a darting run into the area.
His manager Arsene Wenger has been more than impressed by the 18-year-old's progress following an operation on his shoulder during the summer.
Wenger said: "He has found the injection of pace he had before and he uses his body better.
"When you see what he brings when he came on, you are very excited.
"I see him playing through the middle eventually, but I played [Alexander] Hleb there today because there was so little space.
"Certainly Theo has benefited mentally rather than 'footballistically', but maturity-wise it helped him."
Wenger reflected: "He saw how little forgiveness there is when you don't perform. As a young kid, you don't imagine football is like that.
"You need to give people time and allow them to see what's important in the game.
"Everything was new for him last year, but he is growing into a man now.
"It has all happened very quickly and now he has realised things are not always easy in life and football.
"I wasn't worried because it looked like his feet were on the ground.
"He has character. He looks like he's not naturally aggressive, but he responds when he has to."