Glamorgan started the day 62 runs in front with Kiran Carlson and Callum Taylor well set and they managed to get to lunch for the loss of just one wicket.
That changed after the interval with Robinson claiming four victims in the space of four overs to set up victory in a match where he took 13 wickets and made 67 with the bat.
Sussex needed 154 for victory, a total they reached with few alarms with Aaron Thomason top scoring with 78 not out.
Sussex didn’t have to wait long for their first breakthrough, Robinson claiming his fifth wicket when Carlson edged him to Thomason in the slips for 132. With Carlson dismissed for the first time in this match Sussex had a chance to wrap up the Glamorgan innings quickly but Taylor and Dan Douthwaite stood firm.
Taylor went past his fifty from 132 balls, an innings that was a stark contrast to his lightning quick hundred on debut last season. Glamorgan reached the lunch break at 336 for six with the chances of a drawn match increasing.
As has been the case throughout this match it was Robinson who made the difference. He was back into the attack for the start of the afternoon session and had Douthwaite dismissed lbw for 26. He repeated this feat with the very next ball, James Weighell trapped in front to bag a pair on Glamorgan debut.
Robinson picked up the last two Glamorgan wickets, returning the best first class figures by an England qualified player since Chris Woakes took nine for 36 against Durham in 2016. The last man out was Taylor for 84 from 251 balls.
Glamorgan started well in the final innings with Michael Hogan getting Tom Haines caught at first slip by Andy Balbirnie for two. The only other success for Glamorgan came when first innings centurion Stiaan van Zyl edged David Lloyd to Chris Cooke for 12.
From there it was all Sussex as Aaron Thomason made his second fifty of the match with Tom Clark finishing on 54 not out in a partnership that was worth 112.