Despite the draw, Spurs crashed out 3-2 on aggregate after losing the first leg in Belgium 1-0 a week ago.
Spurs had things going their way when Christian Eriksen handed them a 1-0 lead and drew them level on aggregate with only 10 minutes into the game.
But Harry Kane’s attempted clearance via a header accidentally found his own net and drew the visitor’s level in the 20th minute.
Things went from bad to worse in the 39th minute when Dele Allif was deservedly shown a straight red card for a horrendous tackle on Brecht Dejaegere.
Despite the numerical disadvantage, Mauricio Pochettino’s men came out of the tunnel for the second half a different team. Looking more threatening and playing with more intent.
It was no surprise when Harambee Stars skipper Wanyama bulleted Spurs’ second into the net in the 61st minute to restore the lead.
As Spurs looked revived and determined for the decisive goal, Jeremy Perbet equalized for Die Buffalos and the visitors hung on till the final whistle to progress to the last 16.
Wanyama became the first African player to score for Spurs at Wembley Stadium.
This was the 25-year-old’s third goal in Spurs’ colours since arriving from Southampton.