Batting first Greenwood and Carlyon have Serbia little hope as they set about taking their bowling attack apart.
Carlyon smashed 10 sixes and four fours in his impressive innings as he became the first Jersey batter to make a century in a T20 international.
Wellington opener Greenwood’s 85 not out off 52 balls. was the joint fourth-highest Jersey score in a T20.
The partnership was ended when Carlyon was run out in the 17th over, with Jonty Jenner being caught for a duck off the next ball.
Zak Tribe hit nine off eight balls before being caught off the penultimate ball of the innings as Jersey ended on 233-3.
They then continued to dominate their opponents with Simo Ivetic (14) and Luka Woods (21) the only Serbian batters to make double figures.
Greenwood took 3-8 while Ben Ward and Charles Perchard each took two wickets as Jersey began with a statement victory.