The Saints, ranked No. 4 in Class 2A, improved to 11-5 overall and 1-0 in the Illini Prairie Conference. Unity fell to 10-8 and 0-1.
"I thought our kids played hard," said Saint coach Jason Welch, whose team has won 11 of its past 12 games. "I thought they played a good game. I thought our guys kept their poise."
Welch praised the play of his son and Nelson.
"They did a good job tonight," he said. "We started going inside more and we did a nice job of getting the ball to Tommy. J.T. did a nice job of working off those other kids."
Central hustled to a 16-8 lead after one quarter. The Saints stretched the gap to 34-21 by intermission and took a 48-32 lead into the final period.
"We defended well," Welch said. "I think that's a sign of a good team when the ball isn't going in as well as you might like."
Unity received 15 points from Jared Routh.