Sussex 203 (Hudson-Prentice 59, Harris 3-38, Swepson 3-52) and 27 for 1 need another 332 runs to beat Glamorgan 242 and 319 (Northeast 104, Carlson 59, McAndrew 4-47)
Glamorgan captain Kiran Carlson changed the tempo of the innings with his half century at faster than a run-a-ball, before leaving it to Northeast to finish the job with 104 and set things up nicely for the final day's play.
The victory target is a tall order in 113 overs on a wicket that remains hard to score on, as Sussex finished on 27 for 1, losing opener Tom Haines caught slip off Australian leg spinner Mitch Swepson. Sussex trail by 331.
Australian Nathan McAndrew was the pick of the Sussex bowlers getting his second four wicket haul of the match, while off spinner Jack Carlson toiled manfully through 28 overs for a return of 1-92 as the rest of the wickets were shared.
Glamorgan batted themselves into a strong position with a mixture of the tortoise and the hare.
Opener Zain-ul-Hassan provided the slow and steady part to set the platform for captain Carlson, who injected some pace into the batting by getting 59 off 50 balls.
Ul-Hassan added a mere 23 runs through the entire morning session as he progressed to 47 at the lunch interval, but even though it was slow it was also important with the Sussex bowlers finding a bit of hitherto unseen bounce in the Sophia Gardens wicket.
He lost opening partner Andrew Salter early, while number three Thomas Bevan departed for 15, Aristides Karvelas and McAndrew getting the wickets.
Northeast is usually fluent when getting his runs, but he too was watchful while progressing steadily through to the lunch interval.
Ul-Hassan departed first ball after the interval to a shot of unusually aggressive intent against Sussex off spinner Carson, and at that point the game changed with Carlson walking to the wicket.
He immediately unveiled an array of shots, happy to go over the top and also employ the reverse sweep, clearly intent on ensuring Sussex would bat before the day was out.
A swipe across the line to occasional medium pacer Tom Haines saw him depart LBW, while a series of Glamorgan batsmen came and went while trying to get Northeast up to his hundred.
Having gone through to that landmark with a series of big hits, Northeast was the last man out for 104, run out trying to keep the strike with the declaration imminent.
Sussex's bowlers rotated their efforts and retained reasonable control apart from the period when Carlson was batting, Australian McAndrew the pick of the attack. They spurned the new ball and bowled more than 100 overs with the old ball.
Then openers Tom Clark and Tom Haines would have been delighted to see out the final overs to keep 10 wickets intact for the final day, but Haines did not look comfortable against Swepson even before being dismissed.