Bowyer put the icing on an outstanding performance by netting the 16th-minute decider after latching onto a pass from James McFadden.
The former England midfielder has made a big impact since initially moving to the West Midlands on loan in January and then completing a permanent move from Upton Park during the summer on a free transfer.
McLeish said: "The goal was the one bit of class we produced in the game. It was trademark Lee Bowyer.
"It was a late run onto a great pass and the execution was world-class.
"When Lee first came here, I got some people raising their eyebrows saying his legs had gone and he was not the same player.
"But he has proved a lot of people wrong. He can run all day, has class about him, and is a real leader."
City have now taken eight points from the last 12 to climb away from the bottom three.