Durham had a first-innings lead of 149 with Alex Lees finishing undefeated on 182.
Four early Glamorgan wickets gave Durham some hope of claiming victory but the stand between Cooke and Carlson took the home side to safety with the teams shaking hands with 16 overs unbowled.
Durham will be left ruing the bad weather that took so much time out of this game on the first two days as they were the team best placed to push for a positive result.
Durham resumed their first innings 114 runs in front with seven wickets in hand. In a madcap first hour they went from 351 for three to 383 all out. The destroyer in chief was Salter who finished seven wickets, his first five-wicket haul in the format, as the Durham middle and lower order attempted to press home their advantage with quick runs.
Salter dismissed David Bedingham in the second over of the day, well stumped by Cooke with a ball that appeared to swing away from the batter. What followed was a succession of Durham players giving away their wickets with attempted big shots.
As his side collapsed around him Alex Lees stood firm, carrying his bat for the second time in his career on his way to his highest first-class score for Durham. While a quick conclusion of the Durham innings may not have been their plan as they started out the final day of this match it did give them more time to claim the 10 Glamorgan wickets they needed for victory.
In the 14 overs they bowled before lunch Durham claimed three Glamorgan wickets with the home side still trailing by 116 at the break.
It could have been four wickets before the interval but Paul Coughlin put down a relatively simple chance at third slip that would have dismissed Colin Ingram without scoring.
While the morning session was hectic, things settled down after lunch. Durham had Glamorgan 66 for four when Ben Raine had Ingram bowled but a partnership of 90 between Carlson and Cooke took Glamorgan into the lead.
It was a breakthrough year for Carlson in 2021 with the Welsh batter scoring 928 first-class runs at an average of 48.84 and he was playing exceptionally before edging one through to the wicketkeeper on 61 off the bowling of Matty Potts.
Glamorgan will be hoping for more eye-catching innings like this one in 2022.
Cooke made 59 in the first innings and was 85 not out in the second, those runs combined with the 205 not out he made in the last match of the 2021 season mean it is an impressive run of scores for the Glamorgan wicketkeeper.
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