The Taunton wicket had already proved one for the batsmen with Ian Bell making 172 for Warwickshire in the first innings.
Somerset resumed from their overnight score of 70-0 and added thirty four more runs before Marcus Trescothick was caught by Darren Maddy off the bowling of Chris Woakes.
The former England international was out for 52 and with the score on 118, Suppiah was caught by Frost from the bowling of Jimmy Anyon.
Langer and Hildreth rallied and put on 225 for the third wicket which saw Langer trapped LBW by Woakes for 76.
At stumps, Hildreth was 191 not out and Somerset on 474-4.