Llorente headed home an 87th-minute winner after earlier producing a shocking miss, while Son had provided the perfect homecoming present by equalising on his first appearance back from international duty with South Korea at the Asian Cup.
Spurs were heading for a third successive Premier League defeat at Wembley after trailing to Craig Cathcart's first-half header, but their turnaround strengthens their top-four position in a round of games where results have gone in their favour.
Llorente's spirit will also have been lifted after atoning for an embarrassing miss, where he somehow put the ball over the crossbar from just three yards out.
The Spaniard has had a tough gig at Spurs, stuck in Harry Kane's shadow, but Pochettino has been impressed.
"I was so happy. Normally I never celebrate goals but today I felt a bit of freedom to celebrate because we deserved to win," he said.
"I am so happy because Fernando worked so hard, working the last four games with Harry Kane out, he's working so hard for the team, to help the team to win three points today is a massive thing.
"Always it builds the confidence in a striker and more when you are competing with Harry Kane, or behind Harry Kane, one of the best strikers in the world, always it's difficult.
"Always you need time. But in all this time he's been a fantastic professional and always was pushing and helping the team."