Spurs had survived a major scare in the previous qualifying stage last week, coming from behind to beat nine-man Lokomotiv Plovdiv with two late goals in Bulgaria.
And the trip to North Macedonia threatened to prove similarly troublesome when Valmir Nafiu cancelled out Erik Lamela's fifth-minute strike.
A visiting team including debutant Joe Hart and the returning Dele Alli toiled for a time until Son Heung-min - fresh from a four-goal salvo at Southampton - restored the lead and then turned provider for Harry Kane, whose goal ensured a play-off with Maccabi Haifa.
Lamela's opener looked to have teed up a straightforward evening for Tottenham, found completely free by Son on the right side of the area to slide a calm finish inside the bottom-left corner.
Spurs dominated but did not threaten again until Toby Alderweireld headed narrowly wide in the 26th minute, with Kostadin Zahov then saving Alli's scruffy eight-yard effort.
Further Tottenham openings followed in the second half without causing Zahov undue concern and Shkendija were level against the run of play after 55 minutes.
Ljupco Doriev fizzed a pass right to Nafiu, who arrowed a sensational effort high past Hart into the top-right corner.
Kane, Giovani Lo Celso and then Lucas Moura were called from the Spurs bench, yet the England captain followed Lamela in squandering a big headed chance with the goal gaping.
Son was clinical when his chance came, though, controlling as Zahov parried Lucas' shot and firing into the roof of the net.