Andreas Weimann struck in the 92nd minute to secure three points for the Villans, which will have eased any lingering relegation fears and may help appease the Villa Park faithful
A tight match against the improving Cottagers was only decided in stoppage time thanks to a goal from substitute Andreas Weimann, who scrambled home after Mark Schwarzer had spilled a Gary Gardner shot.
And McLeish was delighted to have achieved maximum points on home soil with a "great performance".
"It is always fine lines," he told the club's official website. "All the games we've lost have been fine lines but we've lost them and that is the be all and end all, are you winning.
"We will take a bit of praise when we deserve it and we deserved it because it was a great performance.
"I think it was the best performance at Villa Park this season. Maybe Norwich was close to it. Arsenal was very good but we didn't win.
"This was the best because we won. It gets rid of the cloud about not winning at home."
Aston Villa can be backed at 1.74 with 188Bet to claim another home win when they face Bolton on March 20.
McLeish, who was booed by sections of the home support for substituting Charles N'Zogbia during the second period with the match still goalless, also praised his side for keeping going right until the end, and spoke of his "relief" at ending Villa's run of home games without a win.
"The relief was palpable," he added. "That is what it is like in the dug-out, sometimes relief, and you are only really relaxing and not feeling any pressure when you are three or four up.
"But it was right to the wire, we kept going, we persevered, good traits there for improving things, and Andreas came good."