The South Korean eased the pressure on himself by scoring for the first time since the opening game of the season to help secure victory over his former side
The striker netted a hat-trick - his first ever in the Bundesliga - while Stefan Kiessling and Gonzalo Castro also scored as Bayer came out on top at the end of a thrilling encounter.
Son, whose 12 goals in 33 league games last season earned him a €10 million move from Hamburg in June, was delighted to have kick-started his Leverkusen career, though he was quick to express his sympathy for his former employers.
"It was the perfect day for me," the 21-year-old told Bild. "I'm happy that we won.
"But, of course, I'm also a bit sad [after scoring against Hamburg]."
Son had scored only once in his opening eight appearances for Leverkusen as he struggled to make an impact at his new club.
However, head coach Sami Hyypia insisted that he never had any concerns about the South Korea forward and knew he would eventually deliver for his side.
"I told him during the week: 'I trust you. Clear your head,'" the former Liverpool defender said. "Today, he has shown that he is a giant."
Leverkusen sit third in the Bundesliga with 28 points, four behind leaders Bayern Munich.