Heung-Min Son and Georges-Kevin Nkoudou were also on the scoresheet at Wembley as a weakened Spurs team easily beat their Cypriot opponents.
Serge Aurier slammed a low 20-yard shot just wide in the opening minutes as Tottenham dominated the early stages with Son also going close to breaking the deadlock.
Spurs should have taken the lead in the tenth minute when Llorente’s header was only palmed away by Apoel Nicosia goalkeeper Nauzet Perez to Davinson Sanchez whose effort hit Jesus Rueda on the line.
Llorente then almost scrambled the ball home from a cross but Mauricio Pochettino’s side finally did score the opening goal in the 20th minute.
Aurier pulled the ball back for Llorente to fire a left-footed shot home from six yards out.
Spurs continued to pour forward and Son doubled their advantage eight minutes before the break when the South Korean played a one-two with Llorente before firing a low drive into the corner of the net.
Apoel almost reduced the deficit at the start of the second half when a deflected Praxitelis Vouros shot flew just wide of the post.
Danny Rose had to be substituted with what appeared to be an eye injury while Nkoudou added a third goal in the 80th minute with a deflected strike as Spurs returned to winning ways after a recent barren run in the Premier League.
Darren Ferguson declared his delight at a 'big win' for Doncaster after they saw off Bradford 2-0.
Doncaster took a major step towards securing their Sky Bet League One survival by beating Bradford 2-0.
Southampton manager Mark Hughes was delighted to see his new side reach the FA Cup semi-finals but also warned that the Premier League remains a concern.
Borussia Dortmund winger Andre Schurrle was delighted with the team's hard-fought 1-0 Bundesliga victory over Hannover 96 on Sunday afternoon.