Former Leeds United and West Ham midfielder Lee Bowyer scored the all-important goal in the 16th minute as the Blues moved four points clear of the bottom three and level with Roy Hodgson's Cottagers team.
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 wasn't the same player.
"But he's proved a lot of people wrong. He can run all day, has class about him, and is a real leader.
"Today was an indication of the type of player we've got here, people who are prepared to put themselves on the line.
"On many occasions you see players turning their back on the ball, but the guys here throw everything into the challenge.
"We don't want to be defending desperately every week but it's comforting for me to see we've got players who can do that sort of thing. It's all part of the make up of a Premier League team."