Villa remain bottom on the table on four points after 11 games. Their only win of the season came on the opening day away to Bournemouth.
Despite playing on front of their new manager for the first time, Villa fell behind after three minutes when Mousa Dembele overpowered Irish international Ciaran Clark.
They were 2-0 down at half time as Dele Alli scored in added time from the edge of the box. It was the England international's second league goal of the season
Garde's side scored through Jordan Ayew with just over ten minutes left, but conceded in injury time through a Harry Kane goal. Villa have now conceded three goals at least three times in the league this season.
The new manager will be on the sidelines for the first time this weekend as Aston Villa face league leaders Manchester City on Sunday.
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