Chris Cooke and Shubman Gill both made impressive hundreds as Glamorgan put themselves into a strong position, before Ali Orr and Tom Haines scored quickly in response in the final session of another rain-affected day.
Gill scored 119 – his first LV= County Championship hundred – and Cooke 141 as they piled up 533 for eight declared on the second day at the 1st Central County Ground.
Sussex responded positively and were 86 for one when bad light forced the players off with 13 overs still to be bowled at Hove after there had been two short rain delays earlier in the day.
Glamorgan need to win to have any chance of overhauling Middlesex and claiming the second promotion place from Division Two and although Sussex bowled well in the morning session when they took three wickets, Cooke led the charge as he made his tenth first-class century.
Earlier it had been Gill who went on the offensive. He quickly added the nine runs he’d needed overnight to lodge his seventh first-class hundred before hitting for three boundaries in quick succession.
Off-spinner Jack Carson responded in his next over when he tossed another one up and Gill picked out long on, having faced 139 balls and hit 16 fours and two sixes.
Left-armer Sean Hunt had already broken through when he yorked Billy Root and Carson picked up a second wicket when he gave the ball air again and Andrew Salter was also caught at long on.
When Sussex took the new ball Brad Currie soon had James Harris caught behind for 34, after Harris had added 77 with Cooke. Timm van der Gugten helped the South African put on 41 for the eighth wicket before van der Gugten was held at long leg off Tom Clark.
Acceleration came either side of tea as Cooke and Ajaz Patel thrashed 96 in 13 overs with Patel hitting an undefeated 51 from 37 balls including three sixes, two of them hit over long-on.
Cooke hardly played a false shot before edging Hunt to wicketkeeper Oli Carter after making his second Championship century of the season. His 141 came off 165 balls with 14 fours and two sixes.
Carter was one of two substitutes employed by Sussex after Charlie Tear and Fynn Hudson-Prentice went down ill overnight. The Glamorgan total was also swelled by 50 extras.
Sussex began their reply needing 384 to avoid the follow-on and they made a positive start, Ali Orr and Tom Haines laying into some wayward new-ball bowling from Harris and Mick Hogan.
They added 69 in 11.2 overs before Hogan’s nip-backer struck Orr on the back leg and he was lbw for 45. Haines and Tom Alsop saw their side through to the close but Glamorgan will still feel they can claim their first Championship win at Hove since 1975, even though the pitch shows little sign of deterioration.