Son has endured a difficult season in the Premier League but put those issues to one side to score twice as the South Koreans took a two-goal lead into the interval in Klinsmann's first game in charge of the Taeguk Warriors.
"I'm obviously very happy every time Sonny scores," said Klinsmann, who was appointed as the replacement for Paulo Bento at the end of February.
"As a striker, this is what you're looking for. He had a fantastic game. He has the freedom to rotate (behind the striker). As long as he knows where the goal is, I am happy."
Son has struggled to repeat the performances that saw him finish as the Premier League's joint-top scorer last season, but he gave South Korea the lead from distance in the 10th minute before curling home a stunning free-kick moments before the interval.
However, the South Koreans failed to give Klinsmann a winning start to his tenure when goals from James Rodriguez and Jorge Carrascal in the first five minutes of the second half saw the Colombians claim a draw.
Despite the slip, the former US and Germany coach was encouraged by the performance after only spending a limited time with his squad following his arrival in the country.
"In just a few days, I saw a lot of good things. This game was very, very good," said Klinsmann.
"We gave two goals away right after halftime, unfortunately. Maybe concentration was not there. The rest of the 84 minutes was a very good game.
"We keep learning, and we keep trying things out.
"We wanted to, from the beginning, play high tempo and find ways to get chances, and match the aggressiveness of Colombia.
"And we matched that aggressiveness. I was very pleased with the way we tactically executed our ideas. I am really, really pleased with the performance."
