The 37-year-old has been given only limited opportunities this season and recently revealed he would consider leaving the club, but he was brought in as one of nine changes at St Andrew's and netted the deciding goal in the 3-2 victory 17 minutes from time.
McLeish said: "What can you say about the wee man? He's a world-class finisher. Kevin is a bit of a lucky mascot for me.
"If I'm lucky enough to be a manager for the next 20 years, I'll probably keep signing him."