Ben Slater and Haseeb Hameed's first-wicket stand of 172 offset Somerset's first innings lead despite the visitors' tail finding form on day three.
Migael Pretorius scored a career-best 94 not out from 71 deliveries, while Jack Leach scored 37 to give their side a first innings total of 470 all out - a lead of 110.
But the Notts pair produced a collected response after Dillon Pennington claimed his maiden Notts five-fer to give the hosts a 67-run lead with nine wickets in hand going into the final d