Set 294 to win, MCC finished on 296 for three with 25 balls to spare.
Australia one-day specialist Finch put on 107 for the first wicket with MCC captain Sachin Tendulkar (44) in what could be the retired India great's final appearance at Lord's.
Earlier, Tendulkar's former India team-mate Yuvraj Singh struck a blistering 132 in a total of 293 for seven after MCC had collapsed to 68 for five in the face of Pakistan off-spinner Saeed Ajmal, who finished with figures of four for 45.MCC's captain Sachin Tendulkar leads his team onto the field before a cricket match against a Rest of the World. REUTERS
But fans looking forward to seeing Rest of the World captain Shane Warne bowl against the likes of Tendulkar and Brian Lara were disappointed when the leg-spinner suffered a broken right hand batting when struck by an accidental beamer from fast bowler Brett Lee, his former Australia team-mate.
Marylebone Cricket Club (MCC) moved to its present site of Lord's in the north-west London suburb of St John's Wood in 1814 with the club itself founded in 1787.
MCC's captain Sachin Tendulkar smiles as Rest of the World's Yuvraj Singh attempts to grab his leg. REUTERS
Although it is more than 40 years since MCC ceased to run English cricket, it retains worldwide responsibility for the sport's rules or 'Laws' as they are known.
The starting XI's are as follows:
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