Sussex finished their first innings on 481 all out, 196 runs ahead of Glamorgan As in the first innings of this match, Glamorgan’s top order struggled but Carlson came to the rescue once again.
Ollie Robinson was a class apart, claiming four for 59, but the other Sussex bowlers struggled to match his penetration.
Carlson’s 129 means that Glamorgan go into the last day leading by 62 runs with five second innings wickets in hand.
It took just three balls to wrap up the Sussex first innings with Robinson dismissed for 67 with no runs added to the overnight score.
With Glamorgan having a large hill to climb to bring themselves back into this match they wanted a strong start from their top order. Robinson prevented that from happening, claiming three lbw dismissals before lunch. With Henry Crocombe chipping in with an lbw of his own Glamorgan found themselves four wickets down for 95, still 101 behind.
It was then that Carlson stepped up. He had finished undefeated on 127 in the first innings, and he cruised to another century, this one coming from just 115 balls. While Carlson was finding things easy the same could not be said for the rest of the Glamorgan top order with Chris Cooke lucky to survive when he was dropped on three off the bowling of Jack Carson.
Cooke departed for 12 when he feathered an edge to Ben Brown off the impressive Robinson to leave Glamorgan 150 for five. It was then that Carlson found some support from Calum Taylor as they took Glamorgan into the lead.
With Carlson and Taylor looking untroubled by seam Sussex turned to the spin of Carson and Delray Rawlins to see them to the new ball and they were creating chances. Carson was unlucky not to claim the wicket of Taylor when another chance went down at first slip.
Robinson looked dangerous with the new ball but Carlson and Taylor stood firm, taking their partnership past the 100 mark to reach the close with Glamorgan on 258 for five heading into the final day.
Sussex coach Ian Salisbury praised Carlson's knock and had words of encouragement for Robinson.
"Well played to the young lad [Carlson] he played really well today," Salisbury said. "We haven’t got him out yet! He has played really well, really pleased for him. Just shows that you can bat on this wicket.
"Obviously we got a big score, we didn’t expect them to roll over. After last week they have got some confidence. Ultimately they are going into day four at 62 for five.
Asked about Robinson, alisbury said: "He is pretty decent isn’t he. Ollie is an outstanding bowler, he has proven that now for a few seasons. All he can do if he wants to play for England is to keep doing performances like that. And at the moment he looks, I would say, Test match standard. He is a fantastic bowler."