Nottinghamshire captain Chris Read scored 98 to help earn four batting points and prevent the follow on at Taunton.
Resuming on 77-3, Notts slipped to 147-6 following the quick-fire dismissals of Scott Newman and Samit Patel. Newman had improved his overnight tally of 46, falling lbw to Suppiah for 87, the highest score by a Nottinghamshire opener this season.
Read was dropped by Marcus Trescothick on 41 and took advantage of the reprieve to re-affirm his position as the county’s leading LV County Championship run-scorer.
“Chris played very well and his innings took us past the follow-on and Scott Newman and Mark Ealham also scored important runs,” said Nottinghamshire Director of Cricket Mick Newell.
“Scott has cemented his place for our next two LV County Championship games now and hopefully he can continue to make it work.
“In all probability, we’re heading for a draw now because I can’t see Somerset giving us an opportunity on the final day.”
Somerset had reached 29-0 at the close with Andy Caddick choosing to announce that he will retire from professional cricket at the end of the season.