Sammy King struck an unbeaten 158 as Durham were made to work in tough conditions at Lady Bay.
The 21-year-olds score, which came from 219 balls and featured 15 fours and two sixes, was supplemented by 70 from Ben Martindale, 56 from Sam Seecharan and 66 not out from Jordan Neil.
It left Notts leading by 85 heading into the third day, after Durham declared on 401.
The hosts had resumed 8/2, but century stands between Martindale and Dane Schadendorf (46), and King and Seecharan took the hosts to 288/6.
Those partnerships preceded the biggest of the day between King and Neil, worth 202 across 43 overs by stumps.