The new Sussex loanee picked up three for 22 from his seven-over spell.
After winning the toss and deciding to bowl first, Sussex made an early breakthrough as Steve Magoffin clean bowled Keaton Jennings for five.
Durham fought back well from that point, though, with Mark Stoneman and Scott Borthwick (24) putting on a quickfire 69 for the second wicket.
However, Linley’s introduction into the attack saw a change in fortune for Sussex.
He dismissed Borthwick (24), Stoneman (51) and Paul Collingwood (nine) in quick succession as Durham went from 80-1 to 96-4.
Michael Richardson (31 not out) and Gordon Muchall (19 not out) then saw out the final hour of the session as they put on an unbroken stand of 51 to leave Durham 147 for four at lunch on day one.
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