Somerset's bowlers lacked any penetration on a flat last-day wicket and they had to be content with 12 points from a game they dominated, while Sussex took seven.
Yardy looked solid until, with the score on 155, he edged a drive off Steffan Jones and was well held by Marcus Trescothick at second slip, but by then Goodwin was well set.
The Zimbabwean had a scare on 84 when he edged Zander de Bruyn between Kieswetter and first slip Justin Langer.
But he went on to reach his ton off 169 deliveries, with 10 boundaries, and Adams proved a reliable partner as the pair comfortably saved the match.