Chris Rogers' side were all out for 402 at Uxbridge on Thursday morning and they were further boosted when Tim Murtagh took the wickets of Varun Chopra and Will Porterfield.
From 26 for two, Westwood and Troughton guided Warwickshire to 178 without further loss in a partnership that lasted 60 overs. Westwood will resume on Friday needing just 11 runs for his century while Warwickshire captain Troughton is unbeaten on 60.
Third-placed Somerset faltered badly in their reply against Lancashire at Aigburth.
Captain Marcus Trescothick was dismissed for one in his first championship match since April and only James Hildreth (45) mustered an innings of any real significance as Somerset were all out for 149.
Earlier, Peter Trego and Alfonso Thomas took four wickets apiece as Lancashire were dismissed for 185.
Ed Joyce's century put Sussex in pole position against struggling Worcestershire.
The opener made a tremendous 107 from 260 balls in Sussex's total of 325 for seven, with Luke Wright contributing a fine 78, which contained eight fours and a six.
It could have been worse for Worcestershire, who now trail by 163 runs, but for Alan Richardson taking four for 67.