Durham lost Ian Blackwell in the second over the day when he was bowled by Wright having added four to his overnight score of 130.
Having steered Durham to maximum batting points, and his total to 175 Gordon Muchall was caught by Vikram Solanki off the bowling of Jones in the 100th over.
The new partnership of Phil Mustard and Scott Borthwick, whose fifty came off 77 balls and included three fours, put on 154 with Mustard smashing a boundary to bring up his fifth century for Durham, his first this season, from 136 balls, including nine boundaries.
He was dismissed for 101 when Solanki held onto another catch in the slips, this time off Ali, with Durham 562-7.
Some quick scoring from Callum Thorp, including two huge sixes, Durham declared on 587-7 giving themselves thirty minutes to bowl at Worcestershire before the tea break.
Stephen Harmison struck twice before the end of the second session, Matthew Pardoe caught by Ben Raine (subbing for Dale Benkenstein) at short square leg for 11 and James Cameron caught in the gully by Callum Thorp for 18.
At tea the hosts were 31-2.
Ruel Brathwaite claimed the scalp of Solanki, bowling him for 10 with the second ball of his third over, reducing Worcester to 49-3.
The hosts were 50-4 after a cracking catch from Raine in the covers off Ben Stokes saw Alex Kervezee out for just 1 in the 21st over.
Durham were confident and committed in the field and in unison with some effective bowling kept the Worcestershire run rate to a minimum.
Harmison returned for a second spell with five overs to go and collected the wicket of Ali, who had led a small revival, adding 46 to the Worcestershire total before nicking the ball to Mustard.
At the close of play on day two Worcestershire were 105-5 with Shankar 10* and Andrew 6* Harmison finished the day with figures of 3-27 after 11 overs.