Worcestershire 410 for 9 (Libby 198*, Hose 85) lead Sussex 348 (Carter 76, McAndrew 65, Carson 64, Leach 6-78) by 62 runs
But Sussex fought back admirably in the final hour to take six wickets, four of them with the second new ball.
Libby, though, proved immovable and will resume on Tuesday on 198 out of a total of 410 for nine, a lead of 62. So far he has faced 257 balls and hit 28 fours.
The 30-year-old loves batting at the 1st Central County Ground and against Sussex. Last September he helped himself to 215 and apart from a hard chance he offered to Tom Alsop at slip shortly after reaching his second hundred of the season it was a near-faultless display by Libby, who made a hundred on debut against Sussex for his former club Nottinghamshire back in 2014.
Together with Hose, they accelerated either side of tea in a fourth-wicket alliance of 192 from 33 overs, ticking along at nearly seven runs an over for a spell. Hose contributed 85 off 100 balls with 12 fours and a six but when he was dismissed it sparked a collapse which saw six wickets go for 29 runs in 8.5 overs.
Earlier, as the pitch flattened and the sun came out, there had been marginal room for error and although stand-in captain Tom Alsop, deputising for Cheteshwar Pujara, used eight bowlers and tried different combinations his attack struggled for control.
New Zealander Henry Shipley, on his Sussex debut, took three wickets including Gareth Roderick, promoted to open for the first time in his Worcestershire career. Roderick had put on 52 with Libby when he was caught off bat and pad at third slip and Shipley struck again in his post-lunch spell thanks to a fine take in front of slip by wicketkeeper Ollie Carter to remove the dangerous Azhar Ali for 25.
Jack Haynes also looked to have played himself in when Fynn Hudson-Prentice surprised him with a bit more bounce and Alsop took the catch at slip.
But by then Libby was going through the gears, judging length impeccably and striking the ball fluently all around the wicket, particularly against the six seamers Sussex employed. A back-foot force off Hudson-Prentice for his 17th boundary took him to his second hundred of the season following his unbeaten 104 in the opening game against Derbyshire.
Hose was well into his stride too and when Alsop failed to hold on to a very tough chance offered by Libby on 122 Sussex must have feared conceding a sizeable deficit.
Libby went from 100 to 150 from just 59 more balls before Hose deposited off-spinner Jack Carson out of the ground over long on, having collected nine fours in his 67-ball fifty.
But Sussex kept plugging away and although Libby proved immovable, they hit back strongly after Ibrahim ended the fourth-wicket stand when he sneaked one through Hose’s defences and knocked back his off stump.
Brett D’Oliveira was caught at slip propping forward to off-spinner James Coles and then Sussex made inroads with the second new ball. Ari Karvelas, the best of their seamers, picked up Matthew Waite and Leach in successive overs, both to smart catches at second slip by Tom Clark.
Shipley yorked debutant Usama Mir for his third wicket and Karvelas pinned Adam Finch with late inswing. When last man Ben Gibbon joined him, Libby was on 192 but Worcestershire’s no11 held firm.