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Batting at number five, Stokes came to the middle with Durham 30-3 on day two, in reply to their opponents' 450 all out.
The 35-year-old put on a 153-run fourth-wicket partnership with Will Rhodes.
Stokes was dismissed just after stand-in captain Joe Root and Harry Brook took England past 100-3, chasing an unlikely 463 to beat New Zealand in the second Test.
Stokes and pace bowler Gus Atkinson are under investigation for their part in an incident in a London venue after England's first-Test victory, when they broke the team's midnight curfew.
It is understood the process is progressing to a point where a path for the pair to come back is cleared, although an official announcement may not arrive until the conclusion of the second Test.
While all outcomes remain possible, there is a growing likelihood Stokes is back to lead England for the third and final Test at Trent Bridge, which starts on Thursday.
Resuming on 388-6, Northamptonshire opener Ricardo Vasconcelos reached 187, two more than his previous career high score, before being caught behind off the bowling of Matthew Potts.
The England seamer then bowled Conway and Justin Broad, before Callum Parkinson had Liam Guthrie caught to wrap up the Northamptonshire innings.
Ben Sanderson dismissed openers Alex Lees and Ben McKinney and Conway had David Bedingham caught behind, before Rhodes and Stokes steadied the ship.
Having seen Stokes dismissed by Conway, Rhodes was also removed by the Australian quick for 62, becoming the third player to edge to Vasconcelos behind the stumps.
"It's nice to see how Stokesy goes about his business," said Rhodes.
"It's not often you're standing at the other end and you feel inferior to someone.
"Nobody in the crowd's come to watch me bat so it was nice to go about my work pretty quietly."
Sanderson claimed the wickets of Graham Clark and Kasey Aldridge later in the session, finishing with overnight figures of 4-81 as Durham closed on 302-7, trailing by 148.
