The Togo striker nodded Christian Eriksen's cross home for Spurs' opener before the Denmark international doubled their lead, making Danny Welbeck's strike a mere consolation.
The 2-1 win was Tottenham's second successive victory at Old Trafford, having also won there under the tutelage of Villas-Boas last season.
However, the Portuguese departed White Hart Lane in December after a shaky start to the season that was characterised by a ponderous brand of football, featuring formations with a lone striker.
That resulted in few first-team opportunities for Adebayor, who also fell out with Villas-Boas over late returns from international duty.
But the 29-year-old has been reborn under new coach Tim Sherwood, scoring three goals in his last four games - helping Spurs to three wins in the former midfielder's opening four league games in charge.
And Assou-Ekotto - on loan at QPR after also seeing his chances dry up under Villas-Boas - believes Adebayor has proven the former coach wrong with his sparkling performances.
He tweeted: "I luv my man adebayor... He just show how AVB was wrong about him...Well done spurs."
