Resuming on 111-4 with a lead of 145, Simpson and Ibrahim were tested by Potts and Ben Raine.
Sussex continued their plan of taking time out of the game, with the pair rarely letting their rearguard action slip in the first hour.
Potts had a couple of lbw shouts against Ibrahim turned down as the Durham quick searched for a breakthrough.
The first hour was successfully negated and Ibrahim then brought up his first half-century of the season from 161 deliveries, while skipper Simpson pulled a Conners ball for four to reach his 50 from 106.
Things continued in the same vein after lunch, with the Durham bowlers toiling while Sussex were happy to edge further towards the draw.
Ibrahim did punish any freebies offered by the bowlers as he pulled a Will Rhodes short ball for four, but he survived an lbw shout from Raine when Durham took the second new ball.
He then responded by playing a delightful cover drive off the bowling of Raine, but the Durham man was testing the 20-year-old.
Simpson was also having a difficult time against Potts, with the England man sending a couple past the Sussex captain’s outside edge, but he responded by playing a crunching cover drive off Raine for four.
Potts came so close to a breakthrough, but Ollie Robinson dropped Simpson on 77 as the Sussex skipper gloved one down the legside, but Conners got him soon after when he chipped one up in the air and Lees produced an excellent catch at mid-off.
Ibrahim then reached his first century of the season from 264 deliveries with a single on the legside, having recently made a big hundred for the second XI.
He guided his side to tea alongside Fynn Hudson-Prentice, who tried to be aggressive after the break but Drissell bowled him for 26 as he missed one completely.
That brought Jack Carson to the crease, who was there with Ibrahim when the two sides settled for a draw.
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