The pair added just nine runs to their partnership of 326 as Durham fought back well with the ball following their mauling the previous afternoon.
With rain also delaying the game by 45 minutes Sussex were only able to add 64 runs to their overnight score of 441-5 as they reached lunch on 505-9.
Wright surpassed his previous career-best first class score of 187 before he was caught behind off the bowling of Chris Rushworth for 189.
Ashar Zaidi’s poor start to the season continued as he fell in similar fashion to the same bowler for a duck two balls later.
Mark Wood then ended the near five-hour innings of Brown when he clipped his off bail. The Sussex wicketkeeper’s score of 163 was the highest by a No.7 in the club’s history.
James Anyon hit a quickfire 23 before he became Wood’s second victim of the morning but Steve Magoffin (15) and Jon Lewis (8) survived until lunch.