Having made only three in the first innings, Cook was caught at mid-wicket for five off Jack Brooks (3-22).
Adil Rashid took 4-72 as MCC were bowled out for 220 in their second innings, despite Nick Compton's 74.
First-innings centurion Adam Lyth made 46 not out as Yorkshire eased to victory with a day to spare on 73-1.
Cook did not even manage a boundary in his last competitive knock before England head to the West Indies.
Last week, Yorkshire coach Jason Gillespie said Cook's inclusion in the MCC team was a "win-win for everyone".
The Essex opener went into the annual Champion County first-class fixture after making 35 in last Friday's T20 match against Sussex - his first competitive innings since losing the England one-day captaincy.
Having resumed on his overnight score of two, Cook fell to the first delivery of the day's seventh over as Brooks made the Tykes' first breakthrough.
MCC, who began the day on 13-0, recovered after losing Cook early as Michael Carberry (23), James Hildreth (49) and Compton gave them a second-innings lead.
But Rashid helped wrap up the innings and leave Yorkshire a victory target of only 70, which they passed with ease as Lyth hit seven fours in his 65-ball knock.
England Test captain Alastair Cook suffered his second failure of the match as county champions Yorkshire beat MCC by nine wickets in Abu Dhabi.