Sussex scored 391 runs for 4 wickets against Derbyshire, with a standout performance from Hughes who scored 144 runs. Haines also made a significant contribution with 72 runs, while Alsop remained unbeaten on 69*.
Australian Daniel Hughes made 144 as second division leaders Sussex established a strong position after day one against Derbyshire at Hove.
Derbyshire elected to bowl first then saw Hughes and Tom Haines put on 196 in just 36 overs. Haines made 72 and after Hughes departed Tom Alsop hit an unbeaten 69 as Sussex closed on 391 for 4.
It was just the response they would have wanted after losing only their second game of the season to promotion rivals Yorkshire last week.
They began the game six points clear of second-placed Middlesex and nine ahead of Yorkshire, who are playing each other at Headingley, but three of their remaining four matches are at the 1st Central County Ground where they won three out of four this season and know the conditions well.
Once again there was a good covering of grass on the pitch which would have influenced Derbyshire skipper David Lloyd's decision to insert Sussex but his seamers, armed with the Kookaburra ball which is being used for the next two rounds of Vitality County Championship fixtures, struggled for consistency, particularly before lunch, and Hughes and Haines cashed in.
It wasn't until deep into the second session, when spinners David Lloyd and Jack Morley operated in tandem, that the run rate dipped below five an over but by then Sussex had taken control.
Hughes offered one chance on 35 when he drove at Zak Chappell, but Derbyshire skipper Wayne Madsen couldn't hold on to the edge diving to his right at second slip, and by lunch the two left-handers had plundered 161 from 28 overs, targeting the short boundary on the scoreboard side.
Hughes duly eased to the ninth first-class hundred of his career just after lunch and it was a surprise when he fell for 144 off 142 balls. South African Daryn Dupavillon had bowled a wide earlier in the over when he speared another delivery outside off stump which Hughes could have ignored, but instead under-edged to keeper Brooke Guest. Hughes hit 18 fours and three sixes, but it was a somewhat tame end to an excellent innings by the 35-year-old from Sydney, who has already confirmed that he will return to Sussex next season. It was also the 1500th century scored against Derbyshire in all formats.
Haines had already departed for a fluent 72 when Chappell tempted him into a loose drive and this time Madsen held on at slip while Tom Clark, one of the five left-handers in Sussex's top six, squandered a promising start when left-armer spinner Morley found extra bounce and the edge looped to slip high off the bat.
But by then Alsop was easing to his seventh half-century of the season as he added 66 for the fourth wicket with James Coles, who looked untroubled until he played across the line to off-spinner Lloyd. Alsop has yet to convert any of those fifties into a hundred but he won't have a better opportunity when he resumes tomorrow, having so far put on 39 for the fifth wicket with captain John Simpson, who was dropped by Madsen off Dupavillon on 21 late in the day.