Smith was still there at the close on 120 alongside Jordan Clark on 34, with the visitors having reached 312 for five despite losing opener Dom Sibley for just three.
Tom Helm’s three for 86 helped to peg back some ground, but Surrey left the field the happier.
Former England captain Sir Alastair Cook hit an unbeaten 64 as Essex closed to within 101 of Kent with 10 wickets in hand after an eventful opening day at Chelmsford.
Jamie Porter and Sam Cook took three wickets each as the visitors, who elected to bat, were skittled out for just 207 in 59 overs, with opener Ben Compton’s 47 the most notable contribution.
Cook and Nick Browne got Essex’s reply off to a strong start to reach the close at 106 without loss.
George Balderson and Tom Bailey mounted a rearguard action against Warwickshire to edge Lancashire towards 300 with an unbeaten eighth-wicket partnership of 145.
Number seven Balderson reached stumps six runs short of a century with number nine Bailey 75 not out to help the visitors to 295 for seven.
Nottinghamshire will resume against Hampshire trailing by 79 runs with five wickets in hand after an eventful day at Trent Bridge.
Brett Hutton, Dane Paterson and Lyndon James each took three wickets as the visitors were bowled out for 166.
However, Ian Holland claimed four for 19 in eight overs to reduce Nottinghamshire to 87 for five.
Northamptonshire seamer Jack White’s five-wicket haul could not prevent Somerset reaching the 350 mark.
White claimed five for 77 at the County Ground as the visitors were eventually dismissed for 351 with opener Sean Dickson top-scoring with 70 and George Bartlett making 55.
In Division Two, Derbyshire wicketkeeper Brooke Guest frustrated leaders Durham with a career-best 145 not out as the home side ended day one 317 for six after being put in.
Number three Guest hit 22 fours in an unbeaten 257-ball stay and put on 118 for the third wicket with Wayne Madsen, who made 62, before Durham skipper Scott Borthwick took two late wickets to edge his side back into it.
England spinner Rehan Ahmed provided some much-needed resistance as Leicestershire attempted to avoid a significant first-innings deficit against Worcestershire at Oakham.
Ahmed made 25 not out as the home side slumped to 88 for eight in response to the visitors’ total of just 178.
Matt Salisbury and Wiaan Mulder both took three Worcestershire wickets, but Dillon Pennington matched the feat at a cost of just 24 runs as the hosts crumbled.
Yorkshire’s Matthew Fisher took four for 53 as Sussex were reduced to 120 for six on a rain-affected day at Headingley.
Fynn Hudson-Prentice and Nathan McAndrew ended a day on which only 42 overs were bowled unbeaten on 29 and 25 respectively.