Tamim, who made 128 against West Indies in St Vincent last year, showed no sign of nerves as he brought up his second Test century by gloving a boundary to fine leg off Zaheer.
John Hastings then fell to Panesar and Keath went four runs short of a maiden 50, gloving a pull behind off Collingwood, before Strauss brought himself and Middlesex team-mate Eoin Morgan on to bowl 'declaration' spin at each end.
After a rain interruption and tea, Justin Kemp was lbw on the back foot to the left-arm spin of Ian Blackwell and Thomas picked up the important wicket of Van Jaarsveld, caught behind gloving an attempted hook.
Notts resumed the day on 55-3 in response to Somerset's first-day 138 and the visitors enjoyed a great start when Willoughby struck in his first over, Bilal Shafayat gloving behind without adding to his overnight total of 19.