Durham 164 and 380 for (Richardson 129, Jennings 113*) lead Sussex 328 by 216 runs
Keaton Jennings and Michael Richardson both scored hundreds as Division One champions Durham fought back on the third day at Hove to give themselves the chance of ending the campaign with their 11th win.
Sussex looked like wrapping up a three-day victory shortly after lunch when Durham were reduced to 120 for six, still 44 short of making Sussex bat again. But opener Jennings and his partner put on 218 in 56 overs to help the visitors to 380 for 7, a lead of 216.
Jennings batted all day to register his third first-class hundred of the season and second in the Championship, finishing unbeaten on 113, while Richardson lodged a career-best 129 before falling shortly before stumps.
Jennings held Durham's top order together during the morning session when they lost five wickets, three of them to the impressive Chris Jordan who got a surprising amount bounce and carry out of a pitch which has lost its venom of the first two days.
He struck in his second over of the day when Mark Stoneman mistimed a pull and was caught at mid-off. In the next over Steve Magoffin bowled Scott Borthwick with a ball that kept low and Durham were 35 for 3 when Luke Wright came into the attack to end Will Smith's final innings for the county as he slashed at a ball well outside off stump and was caught in the gully.
Ben Stokes counter-attacked impressively with 45 off 40 balls, although he was badly dropped at fine-leg by Magoffin off a top-edge on 24. Twice he deposited James Anyon into adjoining gardens and hit seven fours but when Jordan was summoned back into the attack, his pace proved too much for Stokes, who lost his middle and off stumps.
Paul Collingwood fended a rising delivery to gully and Durham were six down just after lunch when Jordan superbly caught Phil Mustard at slip high above his head off Anyon.
It was to be Sussex's last success for more than three hours as Jennings and Richardson rebuilt the innings. Sussex were hampered by the absence of their front-line spinner Ashar Zaidi, who was off the field after breaking a finger batting on the second day, and as the seamers tired Durham were able to start building a decent lead.
Sussex took the new ball immediately as it became available and Anyon eventually broke through to claim his 50th Championship wicket of the season when Richardson's tired pull lobbed up to mid-on.
It was revenge of sorts for the bowler who had twice been hit out of the ground by Richardson, who struck a third six off Chris Nash and 16 fours in an innings that spanned 178 balls.
But the wayward Anyon was soon suffering again when Usman Arshad struck four boundaries off the penultimate over of the day to push Durham's lead beyond 200.