The 36-year-old, who is playing in what could very well be his final Test appearance in England, boasted an innings of 147 to move onto the famous honours board.
"It's something I've always wanted to do," Sangakkara told Sky Sports News. "Coming on this tour, which might be my last Test tour to England, I just wanted to enjoy it. If it happened, it would happen.
"I just did a bit of preparation, changed a bit in my technique right from the start and I'm pretty happy it worked. It's a very special place to play your cricket at, and Sri Lankans have done pretty well individually here. It feels very special to get on the honours board."
Sri Lanka ended day three of the first Test on 415-7 compared to England's 575-5.