The Slovak surged clear on the uphill finish to win the 212.5km third stage from Verviers in Belgium to Longwy.
But he credited his brother Juraj, the Slovak national champion, for working hard all day for his Bora team.
"It's very nice, I'm very happy for him because he can feel also the atmosphere of the Tour de France for the first time," said Sagan, 27, of his 28-year-old brother.
"I have to say thank you to all my team because they did an amazing job, especially my brother, all day in the front pulling to catch the breakaway."
Sagan also said it was his brother who had first got him interested in bicycle racing.
"It's special because he's my brother, we can race on bikes. "For sure without my brother, I'm not here now. It was his idea and after I followed."
One of Sagan's shoes was unclipped in the sprint finish but he kept his cool, re-clipped and pushed on to win ahead of Australian Michael Matthews, with Dan Martin of Ireland in third.
Briton Geraint Thomas kept the yellow jersey after coming home in eighth, one place ahead of his Sky team leader and reigning champion Chris Froome, two seconds behind the winner.
It meant that Froome moved up to second overall, 12 seconds behind Thomas, with Matthews third on the same time and Sagan just one second further back in fourth.
It briefly looked as if Thomas and Froome might be caught out as Australian contender Richie Porte launched an attack some 800 metres from the finish, with even two-time former winner Alberto Contador unable to hold his wheel.
For the most part, the peloton and overall favourites enjoyed a leisurely day in the saddle.
But in the final 60km, three more escapees joined up with the breakaway, whose advantage was down to one minute, and gave it added impetus.
However, the punchers' teams weren't prepared to give them any leeway and Frenchman Lilian Calmejane, the last man standing, was caught with 10km to ride.
From then on, it was up to the specialist punchers and Sagan, once again, proved the strongest.
He also closed in on the green points jersey, still held by Sunday's stage two winner Marcel Kittel of Germany, which Sagan has won in each of the last five years.