Buck blasted 51 from 71 balls, while Luke Procter finished unbeaten on 49 as the County were bowled out for 368, having been 267 for eight.
But Sussex kept control as they added to their 422 all out with a strong start to their second innings, finishing the third day of the Specsavers County Championship Division Two clash on 292 for four.
Phil Salt smashed 122 from just 104 balls to ensure Sussex will go into the final day with a 346-run lead and six wickets remaining.
“The aim was to get batting points and with Luke playing nicely I thought if I could just bat some time the scoreboard would take care of itself," Buck said.
“They bowled well first thing but we got through that and I enjoyed trying to give it a whack to make the lead as few as possible.
“Phil’s inning was very special but the bowlers stuck at it very well."
Salt says Sussex were eager to accelerate early in their second innings.
The opening batsman said: "We had to put our foot down and I thought if I got a few more we’d be in a really strong position.
"We didn’t look too far ahead but we all knew a ball-park figure of where we wanted to be at the close.
"Hopefully we can get a few more in the morning then look to bowl them out.
"It’s a good surface to bat on now and I think we’ll have to bowl really well to win but we’ve got that in us."