The 20-year-old was on hand to turn home in stoppage time after Mark Schwarzer could only fumble Gary Gardner's initial effort.
Weimann replaced Charles N’Zogbia to collective boos from the home support and cries of 'you don’t know what you’re doing' aimed at McLeish, but the Scot’s was delighted to see his decision prove correct.
He told reporters: “The fans were great, they see a forward going off [N’Zogbia] and Charles has been in good form, no doubt about it, but I’ve been wanting to get Andreas Weimann on the pitch at some stage today and I discussed that with my coaches before the game because he’s a goalscorer.
“It’s just fitting him into the team and at the right time, there’s been a few key injuries and Andreas deserved his moment.
“He’s been prolific in the reserve team, he’s a hungry young man, he wants to score goals, he links up with players well. He’s not just a trick in the penalty box, he’s already a good player. His goal record has been exceptional in the reserve team and I felt he deserved a crack at it.”
McLeish recognised his players' lack of cutting edge in the final third after attractive football had got them there in the first place and admitted his team need more efficiency up top.
He continued: “We played some good football, it’s just about being clinical in that last third and there were good moments in that first half where I felt if we’d done something a bit better with the final ball that’s probably the difference from us climbing up the table and I feel there’s a lot more to come from a lot of the players.
“But what a great performance from us, that’s what makes it so satisfying that that was a team of high quality that we deserved to beat today.
“I thought we gave them [the fans] something to be excellent about, we were forcing a succession of shots, keeping Fulham very quiet, we kept some real quality players at bay today.”
A beleaguered Martin Jol however felt the result was 'harsh' on his players and believes the final scoreline does not reflect his player’s efforts.
The Dutchman said: “It was harsh to concede in the final minute. Same against Norwich City of course, we were leading then and we had to settle for a 0-0 today is what I thought. Of course after seeing the first-half it’s a deserved 0-0.
“With the second-half we were the better team, they pressed us high in the first, we couldn’t play around them so we had to change it at half-time and there was no problem whatsoever after that.”
Despite Schawrzer's bad handling, the Dutchman failed to blame his goalkeeper and insisted that bad fortune was to blame for the result.
“No [I don’t blame the ‘keeper]," Jol said. "I don’t blame anyone, in the final minute I feel you have to keep your position and I feel we didn’t do that on the left. It’s always the same, one, two, three mistakes, I think it was a good shot he [Schwarzer] couldn’t handle.”
John Arne Riise went close after the break for the Cottagers, but his effort drifted agonisingly past the wrong side of the post and was one of many opportunities Jol thought his team should have made more of.
He grumbled: “It thought that with Damien Duff before and before that there were two balls across their [Villa’s] goal and no one was there and we should have nicked it probably. Bu that’s what you have to do if you want to get a result away from home.”