Both teams are looking to maintain 100 per cent records and Chris Rushworth???s second five-wicket haul of the season meant Durham just about shaded Tuesday???s play.
Sussex resumed on 115-3 and looked firm favourites when they had reached 217-4, only to slip to 265 all out.
Matt Machan fell for 80 and Luke Wright was bowled for 39 by Rushworth (5-81), who then helped John Hastings (2-57) mop up the tail.
Durham openers Mark Stoneman (41) and Keaton Jennings (38) began the run chase with a fluent stand of 80 before both fell to Ajmal Shahzad (2-40).
But Scott Borthwick (26 not out) and Michael Richardson (7 not out) survived until bad light and rain brought play to an early finish, leaving the match fairly evenly poised and an exciting day in prospect on Wednesday, weather permitting.
Rushworth said: “We knew we needed quick wickets after lunch and to wrap them up like that was a big plus.
“There’s a bit of variable bounce but it’s a good pitch and the scores are about par. It’s been a remarkable game and one of the coldest I’ve played in!???
Defending champions Yorkshire avoided the follow-on against Warwickshire, who now lead by 240 after closing on 108-2.
Having resumed on 128-3, Yorkshire slipped to 249-8 but captain Andrew Gale steered them past the follow-on target with his highest score since last July.
However, having reached 96, he was last man out when he waved his bat wildly at a Boyd Rankin full toss and ballooned a catch to Sam Hain.
Before the catch had been taken, Gale appeared to spread his arms to umpires Steve Garratt and Jeremy Lloyds asking if the delivery had been above waist height but, after consulting, they gave him out.
Gale said later: ???Controversy seems to follow me around.
“I was disappointed to get out but umpires do make mistakes. If this had been a Twenty20 game, I do not think I would have been out, as the benefit usually goes to the batsman.???
Rankin took 6-55 for Warwickshire and Ian Westwood, who made 196 in the first innings, was 48no at stumps.
At the Ageas Bowl, Brendan Taylor made his second Division One century of the summer as Nottinghamshire built up a big lead against Hampshire.
The visitors closed on 296-4 and lead by 391 heading into the final day, having earlier bowled Hampshire out for 276.
Hampshire resumed on 167-4 and slumped to 197-7 but Sean Ervine and Andre Adams both made 31 and added a useful 47 for the ninth wicket.
Zimbabwean Taylor then made the most of an early let-off, Danny Briggs putting a simple chance down at midwicket when he had made just seven.
He went on to score 103 from 120 balls and added 164 for the second wicket with England one-day man Alex Hales, who continued his superb start to the season with 94.
James Taylor will captain the England one-day side against Ireland next week and he reached the close on 53no.
Middlesex need a sizeable 402 to beat Somerset at Taunton and closed on 31-0, Somerset having earlier made 310 in their second innings to build on their lead of 91.
The visitors were bowled out for 317 in their first innings at the start of the day, Lewis Gregory celebrating his call-up to the England one-day international squad by completing figures of ??6-101.
Somerset then merrily went about their business, opener Marcus Trescothick leading the charge with 76 and James Hildreth continuing his fine start to the season with 86, having made 187 in the first innings.
Tom Cooper managed 42 while Ollie Rayner, James Harris and Steven Finn claimed three wickets each for Middlesex, before Nick Gubbins and Sam Robson got their hunt for a very imposing target off to a decent start.
Middlesex off-spinner Rayner said: “We still feel well in the game. This is a??fast scoring ground and James Hildreth has proved for Somerset that, if a batsman??gets in, it is possible for him to make big runs.
“Even if we get tied down for a period, there will??be time to get the required runs.”