Billy Root also contributed a steadfast 43 at the start of the second professional meeting between himself and older brother Joe.
That battle provides an intriguing subplot to an opening round Group Three fixture which started with the Welshmen slipping to 29-3 and 132-7 before recovering to close on 310-8 from 96 overs.
Root and Carlson shared 82 for the fourth wicket either side of lunch before all-rounder Douthwaite and Netherlands seamer van der Gugten united for the eighth wicket either side of tea, sharing 122 – the key partnership.
Douthwaite posted 57 off 90 balls and van der Gugten a career best 80 not out off 134.
In cold and overcast conditions, Yorkshire won the toss and struck three times in the first 12 overs through new ball pair Ben Coad and Matthew Fisher and captain Steve Patterson.
Yorkshire, expected title challengers, let their opponents off the hook, with three catches of varying difficulty dropped.
Fisher rocked back the off stump of opener David Lloyd and later Callum Taylor as they shouldered arms.
Billy Root, who previously faced Joe and Yorkshire in a one-day clash whilst playing for Nottinghamshire in 2017, dropped anchor for three and a quarter hours and faced 126 balls.
Carlson was particularly strong on the square drive, hitting 10 boundaries in 79 balls.
Carlson and Root were two of four afternoon wickets as Glamorgan slipped to 132-7 after 52 overs.
Root was the victim of a superb one-handed diving catch by wicketkeeper Jonny Tattersall off Coad. But that proved to be Yorkshire’s final success until late evening as Douthwaite and van der Gugten changed the face of the day’s play.
Having offered a tough chance to Harry Brook at third slip on eight, Douthwaite was strong off his pads in hitting eight fours to add to sixes off Olivier and Coad.
Van der Gugten was not quite as commanding at the crease, yet he launched Joe Root’s off-spin over long-on for six.
Coad bowled Douthwaite - also shouldering arms - with the second new ball, leaving the score at 254-8.
Michael Hogan also clubbed an unbeaten 40 in a late unbroken stand of 56 for the ninth wicket to further frustrate Yorkshire.
Yorkshire: Lyth, Kohler-Cadmore, Loten, Root, Brook, Tattersall, Bess, Fisher, Patterson (captain), Coad, Olivier.
Glamorgan: Lloyd, Selman, Balbirnie, Root, Carlson, Cooke (captain), Taylor, Douthwaite, Gugten, Hogan, McIlroy.