The pair are two of the club's most experienced players and have helped the Midlands outfit into seventh spot in the Premier League table.
Villa have made an unbeaten start to the new campaign, although drawing five of their seven games means they are eight points behind the league leaders.
McLeish made a ?3.5million swoop for Given from Manchester City over the summer and the ex-Birmingham City boss had no second thoughts bringing in the Irish shot-stopper.
Team-mate Dunne endured an unhappy spell under Gerard Houllier last season, but McLeish is a huge fan of the defender's ability and feels his experience at the back is priceless.
"It was a tremendous deal (for Given). In the past I've missed out on players to make my teams better but this one we were in the right place at the right time," commented McLeish.
"He's such a cool character - experience in terms of a goalkeeper is so vital. He is so calm and you can see he gives that to the team.
"Richard and Shay are on top of the world.
"Dunne's a great player, he's a very experienced centre-back and it's really about players being comfortable in their heads. If their heads aren't right, you can have the best player in the world and they will never kick a ball for you.
"He's an experienced guy so you give guys like that responsibility and they thrive."
Source: Team Talk