Spurs ended a run of five matches without a win in 90 minutes and responded after a poor defeat at Arsenal last week.
Nuno made nine changes to the team that lost the derby and Alli won and converted a penalty inside four minutes.
Four minutes later, Lo Celso doubled their lead with a fine finish from a tight angle as Spurs dominated the first half.
After the break, the hosts struggled and were punished with a stunning volley from Kous after 52 minutes.
Kane was brought on after the strike and produced three fine finishes in 20 minutes to seal a much-needed win for Spurs.