New Zealand posted 179-4 and bowled out Ireland for 91 to secure its fifth straight win over the hosts. The visitors beat Ireland by 31 runs on Monday after a 3-0 series win in the one-day internationals at Malahide.
New Zealand can sweep the three-match T20 series on Friday.
Cleaver's total came off 55 balls and included five fours and four sixes in just his second T20 international appearance. Finn Allen contributed 35 off 20.
Chasing 180, Paul Stirling gave the Irish a fast start, hitting Mitchell Santner for a six and a four in the first over. But against Lockie Ferguson, he was caught to finish with 21 and leave the hosts at 23 for 1.
Ireland managed just four runs for its next two wickets, as Jacob Duffy was dismissed by Gareth Delany for a first-ball duck before Harry Tector (2) was run out.
Ish Sodhi took three wickets for 21 and Ireland was at 86 for seven when Bracewell came on for his first over. The off-spinner had Mark Adair and Barry McCarthy caught in the deep with successive deliveries before Craig Young sliced to backward point from the next ball as Ireland was all out for 91.
Young and Josh Little took two wickets apiece for Ireland.