Llorente, the £14million summer signing from Swansea, had failed to hit the net in his previous 16 appearances for his new club. But the former Juventus striker got off the mark against Cypriot champions Apoel Nicosia at Wembley.
Georges-Kevin Nkoudou and Son Heung-min where also on the scoresheet as Pochettino's men rubber-stamped their dominance of Group H with a 3-0 win.
In the 20th minute Serge Aurier's cross was behind Llorente but he expertly turned his marker and guided his shot past Apoel keeper Nauzet Perez.
"It's important for him," admitted Spurs boss Pochettino. "When you are a striker you need to feel the net. Of course players need time to adapt, when you arrive at a new team with no pre-season you need time to find your best level.
"It's difficult to play 20 or 30 minutes, it's important for him to feel he can cope for 90 minutes.
"He is a player who is going to help the team a lot. He has been helping a lot but now with more confidence and belief he is going to help more."