Needing 262 to win, they wobbled slightly when losing both openers to Ajmal Shahzad after a fluent stand of 80, but were 115 for two when bad light and rain ended play with 26 overs to be bowled.
With Durham needing a further 147 it could still go either way and both sides will hope the weather permits half a day’s play.
Sussex were clear favourites on 217 for four, but they were all out for 265 when last man Matt Hobden was yorked first ball by John Hastings.
This was a clear case of “after the Lord Mayor’s Show” following his last-wicket stand of 165 with Oliver Robinson in the first innings. Robinson’s dream debut also hit the buffers when his first two overs in the second innings cost 16.
The final two wickets of the Sussex innings were scant reward for some exceptional bowling by Hastings, but equally Rushworth deserved his five for 81.
Both were out of luck in the morning, when Harry Finch did well to survive a testing first 55 minutes before surrendering in Usman Arshad’s first over, edging an innocuous ball to Phil Mustard.
Matt Machan abandoned his cavalier approach of the first innings to show surprising resilience in reaching 80 and with Luke Wright playing bold strokes Sussex were in the driving seat until a ball from Arshad which kept low pinned Machan lbw.
It proved a big turning point as wickets fell regularly, the crucial one being that of Wright, who had cruised to 39 when Rushworth nipped one back to take out his middle stump.
With Rushworth and Hastings back in tandem the last four wickets went down for 30 after lunch and with the momentum now in their favour the Durham openers began confidently.
Very little got past the bats of Mark Stoneman and Keaton Jennings with the ball reluctant to swing in the decidedly chilly crosswind.
But three balls after pulling Ajmal Shahzad for six, Stoneman shaped to drive and was lbw for 41 in the 19th over.
Batting suddenly looked much more hazardous and four overs later Jennings propped forward and edged Shahzad to Ben Brown.
As in the first innings, Hobden troubled Scott Borthwick but he was still there on 26 when the elements closed in.