The Portuguese side came into London with a 1-0 lead after last week's first-leg win but Kane's brace by half-time, coupled with an Paços own goal, ensured Spurs' passage into the next phase of the European club football's newest competition.
It was Kane's first start of the season, the day after he announced that he would remain at Tottenham despite a desired move to Premier League champions Manchester City.
The England captain put Spurs up by the ninth minute with a well-positioned strike off of Bryan Gil's expert cross. Kane then doubled the lead in the 34th minute after he pounced on the rebound from Giovani Lo Celso's initial shot.
An own goal by Vitorino Antunes in the 70th minute sealed Paço's fate.
The Europa Conference League is the new third-tier tournament of European competition, below the Champions League and the Europa League.