Cook added just three to his overnight 57 before falling to Kyle Hogg but at lunch on day three they were 252 ahead on 203 for three, with Jaik Mickleburgh (53no) and Mark Pettini (36no) building a damaging partnership.
At Bristol, Jimmy Adams was providing the backbone of Hampshire's innings against Gloucestershire.
Resuming on 165 for eight, Adams and Danny Briggs added 60 runs before the latter fell for a hard-fought 54.
Adams continued along to 129no, including 14 fours and a six, as last man James Tomlinson faced 47 balls for just one run in support.
At New Road, Leicestershire took four morning wickets to leave Worcestershire on 258 for seven.
Off-spinner Jigar Naik claimed all of the scalps to complete a five-wicket haul, but could not get the better of former Sri Lanka batsman Thilan Samaraweera (75no).
- Sports & Recreation
- Jimmy Adams
- Jaik Mickleburgh
- Mark Pettini
- Danny Briggs