Sri Lanka A 332 (Croospulle 128) and 202 for 3 (Madushka 84*, Mendis 67) lead England Lions 405 (Smith 126, Lees 97, Bohannon 54) by 129 runs
Smith's effort surpassed Luke Wright's 91-ball hundred against New Zealand A in 2008-09, and featured 13 fours and eight sixes all told. By the time he was dismissed for 126 from 82 balls, he had formed the backbone of the Lions' 405 in 76.4 overs.
"It is certainly the most entertaining and most enjoyable innings that I have ever played," Smith said afterwards. "I would say it is the best innings that I have ever played.
"I didn't know that it was a record century and I didn't go out there to achieve that obviously. When you get in that situation and you're flying along you are just focusing on being positive and trying to hit boundaries - hit the ball as far and as hard as I can."
The Lions team has been noticeably positive in its approach to batting on this tour, and Smith acknowledged that the success of the Test team under Ben Stokes and Brendon McCullum had been an inspirational factor.
"You definitely take on board the style of play that the England team are employing because that's the style they want to see," he said. "I always knew I had the talent to play that way but to get out here and to do it is really positive for me.
"The coaching staff here give you the freedom to go out and play that way. There are no limits as to what you can do. I'm not focusing on whether I get out, it's about how you can make runs and being positive. That has certainly helped me to make runs here and play the way I did."
At the age of 22, Smith - who is also keeping wicket on this trip - is very much one of the coming men on the county circuit, and was picked for his first Lions tour after playing his part in Surrey's County Championship victory last season.
"It is the next step in my career and it has been an opportunity to show my skills and test myself against some really good bowlers," he said. "It's good to get in this environment and to play against spin and try and adapt my game to that.
"The pitch is pretty flat but the beauty of us scoring so quickly is that it gives us an opportunity and time to bowl them out. We'll aim to do that in the morning and then well hopefully have a chase. We won't fear chasing any total."