Worcestershire then looked to be making steady inroads in their reply at 71-2.
But, with only Kashif Ali stemming the tide, last man out for 55, the Pears then lost their final eight wickets for 41 runs as Matthew Potts claimed 4-29 to bolster his own credentials for selection in the first Test of the summer.
Ben Raine (3-33) and Australia veteran Peter Siddle, with 2-20 on his last appearance, also got among the wickets, while Stokes himself got the key Pears wicket of acting captain Jake Libby.
Durham began their second innings with a 78-run lead but lost three quick wickets before the close.
Alex Lees, home skipper Scott Borthwick and Graham Clark all fell for the hosts, with Smith and Tom Taylor among the wickets.
That left the contest very much in the balance heading into day two as Durham led by 111 runs at the close – but with a distinct chance that this game might be all over by Monday night.
