The Essex batsman has come under scrutiny after three single-figure scores at number three.
But he has been given another chance to nail down a place in the team in what will be England's last Test before the year-ending Ashes series in Australia.
Mark Stoneman and Dawid Malan have also held onto their places after both chipped in with second-innings half- centuries in the five-wicket loss to West Indies at Headingley.
Left out of the starting team in Leeds, Middlesex seamer Toby Roland-Jones and Hampshire leg-spinner Mason Crane will both hope to force their way into the XI for the series decider.
England 3rd Test squad
Joe Root (Yorkshire, capt), Moeen Ali (Worcestershire), James Anderson (Lancashire), Jonny Bairstow (Yorkshire, wkt), Stuart Broad (Nottinghamshire), Alastair Cook (Essex), Mason Crane (Hampshire), Dawid Malan (Middlesex), Toby Roland-Jones (Middlesex), Ben Stokes (Durham), Mark Stoneman (Surrey), Tom Westley (Essex), Chris Woakes (Warwickshire).