The midlands outfit took the lead when Marc Albrighton prodded in Gabriel Agbonlahor's cross and Stiliyan Petrov doubled their advantage with a strike that went in off Gary Cahill. Ivan Klasnic reduced the deficit but Wanderers could not salvage a point as the visitors held firm, demonstrating a resilience that McLeish was particularly pleased with.
"I'm delighted to get the first away win of the season," McLeish said.
"It's been a long time coming - we have thrown away a couple of opportunities, so well done to the players for digging deep at the end under a barrage of Bolton attacks.
"It is credit to their mental toughness, and hopefully that is improving after capitulating at a couple of other away venues."
Bolton manager Owen Coyle - who confirmed Klasnic had come off due to a twisted knee - bemoaned his side's defending and expressed his concern at the attitude they had shown in the first half.
"Disappointment is an understatement, because we were at home and looking to win the game and start moving up the league," Coyle said.
"It is a horrible feeling. I thought the game started evenly with two teams looking quite nervous, but then we conspired towards our own downfall.
"Aston Villa have some very good players, but we made four or five individual mistakes within the first goal - it was self-inflicted.
"Then you are looking for a reaction, for people to show a bit of guts, desire and hunger for the football club, but if the truth be told, for a few minutes, they looked as if they felt sorry for themselves, and that allowed Aston Villa to get a second goal."
Source: PA
Source: PA