Cheteshwar Pujara reached his second double-century since joining Sussex, to give the hosts an excellent chance of securing their first win of the season in the LV= Insurance County Championship.
However, in the final half of the day, an unbroken opening stand of 169 between Alex Lees and Sean Dickson gave Durham a chance of saving the match for the visitors, after they had conceded a first innings lead of 315.
Dickson completed his century just before the close, off 137 balls with 15 fours, while the more subdued Lees finished with 50 not out. Earlier, Sussex had continued to dominate their fixture against one of the favourites for promotion as their overseas stars Cheteshwar Pujara and Mohammad Rizwan put on 154 for the sixth wicket.
Pujara scored 203, his second double century in three matches – and there was another hundred in the other match – while Rizwan found his form on his home debut with an innings of 79 as Sussex piled on 538.
There are enough cracks on the pitch to encourage the Sussex spinners on the final day. But Durham, who are 146 runs behind, feel they have a good chance of a fighting draw on what is still a good surface.
In the first session Sussex scored 128 runs without losing a wicket, which suggests the Durham bowling was poor.
But Durham bowled well in discouraging conditions against two world class batsmen, and there was something heroic about the way Matthew Potts continued to generate pace and bounce bowling downhill from the Cromwell Road end.
The game changed shape dramatically after lunch, when Sussex lost five wickets for 34 runs in nine overs as the slow left-armer Liam Trevaskis followed his 88 runs with figures of five for 128.
That still gave Sussex a huge first innings advantage. But the Durham openers batted superbly in the final session to give their side hope.
The day started with Sussex on 362 for five, with Pujara 128 not out and Rizwan unbeaten on five. Durham probably suspected they were in for a hard time when Pujara rocked onto the back foot and punched the first ball of the morning for four.
The India Test batsman scored just eight runs in the opening 45 minutes, and it was Rizwan who was the busier of the two batsmen, scoring 36 by the time the pair had put in fifty.
There were scares. Rizwan was almost run out by Dickson at point when he was 36 and Pujara, on 140, was close to being caught at first slip. But mostly, it was sublime batting from the two-star batsmen who proved their true worth in a young and depleted Sussex side.
At lunch – which came ten minutes later than scheduled because 13 overs had been missed on the second day - Sussex had reached 490 for five, a lead of 267, with Pujara 186 and Rizwan 74. The 150 partnerships, which coincided with the side reaching 500, came off 149 balls but four runs later Rizwan, pulling hard against Matt Salisbury, was brilliantly caught by Trevaskis at deep square-leg.
Delray Rawlins, got off the mark with a slogged six over midwicket but, pulling, was bowled for 12. Two overs later Pujara, venturing down the wicket to Trevaskis, was stumped. He had faced 334 balls and struck 24 fours. It didn’t last much longer. Henry Crocombe was caught at slip third ball and George Burrows was lbw to the second delivery he received. But the last session belonged to Durham.