Nicolas claimed victory in the Jack Sears Trophy category in the BTCC at Snetterton after a standout showing for EXCELR8 Motorsport.
Nicolas, who has cerebral palsy, became the first disabled driver to compete in the BTCC when he debuted in 2015.
His maiden podium came on the same day Lewis claimed his best result yet for Ferrari with second place at the Canadian Grand Prix.
The result from the younger Hamilton prompted an emotional response from the seven-time Formula 1 champion on social media.
“I could not be more proud of my brother Nicolas Hamilton,” Lewis wrote.
“Seeing the passion and emotion on his face as he stood on his first podium was such a beautiful moment.
“For us both to be on podiums on the same day was major. I called him the second the race ended.
“Motorsport is not built to be inclusive. There is little to no access for people with disabilities, and no support systems to level the playing field.
“This is something so many take for granted. Despite that, despite the barriers and the people who told him it wasn’t possible, he never stopped.
“He fought. He adapted. He proved them wrong.”
Lewis also described his younger brother as an inspiration.
“While he will always be my kid brother, I am profoundly proud of the leader, the athlete, and the man he has become,” he added.
“He inspires me just as much as he inspires everyone watching his journey. No matter how hard it has been he has never given up.
“What he’s achieved is massive and I’m so happy for him. Love you bro, keep going.”
Nicolas was emotional after securing the first silverware of his touring car career.
“I honestly cannot believe what has happened this weekend as I never expected to walk away from Snetterton as winner of the Jack Sears Trophy,” said Nicolas, who finished 17th in the opener before back-to-back 16th place finishes to end the weekend.
“My whole focus was on developing and improving myself, and to end the weekend up on the podium was the most amazing experience.
“I’ve always said that I wanted to win a trophy, but I didn’t want to just be gifted it, and this weekend I feel like I earned it and deserved it.”
The 34-year-old said the achievement marked the culmination of years of hard work and perseverance.
“I’m not going to, but I could happily hang my boots, gloves and helmet up after this weekend knowing that I have achieved the dream of a little boy who was told he would never walk,” he said.
“This is for everyone who has stuck by me and supported me, and even those who have doubted me as it has only fuelled my desire to reach my goal.
“For all those in the disabled community, hopefully this will provide further inspiration of what is possible.”
Contested between drivers yet to score a BTCC podium before the start of the season, the Jack Sears Trophy is named after the championship’s inaugural title winner and remains one of the series’ most respected honours.
