In the morning session, Worcestershire lost two wickets but saved the follow-on with ease to reach lunch on 376-7, just 89 in arrears, thanks to Hose bringing up his first century of the season.
Both Durham wickets were taken by Stokes, who had Henry Cullen caught at slip before dismissing Hose.
Tom Taylor and Matthew Waite put on 85 in untroubled fashion either side of lunch.
But, after Waite was leg-before to Ben Raine for 28, Taylor reached his first fifty of the season before Stokes dismissed him, also leg-before, for 61 to earn his first five-wicket haul in first-class cricket at Chester-le-Street since 2014.
Stokes then completed his best bowling figures in nine years when he had Pears substitute Fateh Singh – on for Usama Mir – caught at long leg by Will Rhodes for 26.
In the fourth over after tea, the Pears broke through when Waite bowled Ben McKinney for 38 with a ball before removing Alex Lees’ off stump off another grubber.
But the highlight came in O’Connor’s sixth over from the Finchale End when he knocked out Agarwal’s off stump.
Ackermann played around a ball from Ben Allison and was leg-before and Warwickshire old boy Will Rhodes lost his off stump to Taylor on 25.
Stokes then came down the pitch and attempted to hit debutant O’Connor over the off-side field, only to sky a catch to Dan Lategan.
But Aldridge (25*) and Robinson (19*) flayed seven boundaries between them to ensure no further damage on 161-6.
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