Not known for his ability as a one-day batsman, Cook's innings was the centrepiece of Essex's 285 for eight in 50 overs with the left-hander striking 10 fours in his 127-ball stay.
Graham Napier, who last month struck a Twenty20 world record 16 sixes in an innings of 152 not out, added late impetus with 61 off just 34 balls.
Yorkshire captain Darren Gough, who had a brief spell with Essex before the former England fast bowler returned to his native county, saw his hopes of a Lord's final in his last season retirement dashed by a batting collapse.
The visitors were bowled out for 198 with Yorkshire losing their nine wickets for 58 runs in 13 overs.
Essex will now play southern neighbours Kent in the final at Lord's on August 16.