England finished the day on 315 for six wickets in reply to the Sri Lanka side's 500 for five declared.
Cook enjoyed a partnership of 77 with captain Michael Vaughan, who hit 38 before being trapped lbw by leg spinner Malinga Bandara.
The only batsman to fail on a docile pitch was Kevin Pietersen who was caught in the gully for four off seamer Nuwan Kulasekera.
Cook, Ian Bell (49), Paul Collingwood (52) and Owais Shah (38) all retired while Ravi Bopara made 40 not out.
England have one more practice game before the first Test starts on December 1 in Kandy.
(Editing by Alison Wildey)