Fellow seamer Tim Southee picked up the other three wickets as Malaysia were shot out for 47 in the group A tie, a target New Zealand surpassed easily in the 12th over well before lunch.
Boult, a left-arm seamer who regards Pakistani legend Wasim Akram as his hero and dreams of becoming a chef, cooked up the second best figures in the history of the tournament.
The 18-year-old fell just one run short of Ben Mendis' 7-19 for Sri Lanka against Zimbabwe at Christchurch in 2002.
Malaysia did not match their winning display against Zimbabwe on Wednesday as five of the top seven batsmen failed to score and no one reached double figures.
The emphatic win ensured New Zealand joined defending champions Pakistan in the quarter-finals from group A at the expense of Malaysia and Zimbabwe.
South Africa stayed on course for the next round from group B with a seven-wicket win over Papua New Guinea at the Kinrara Oval in the Malaysian capital.
Captain Wayne Parnell took 3-19 and Jonathan Vandiar claimed 4-27 as South Africa bowled out the minnows for 125 and then cruised home in the 16th over with opener Pieter Malan making 56.
South Africa ended the league with two wins from three matches, but only an Indian victory over the West Indies on Friday will confirm their place in the quarter-finals.
If the West Indies win, there will be a three-way tie and the two teams with the best net run-rates will advance to the next round.
In group C, Nepal snatched a thrilling three-run win over Namibia in Penang despite a gutsy all-round performance by Louis van der Westhuizen who claimed 2-17 and hit 65 for the African side.
Nepal, bowled out for 164, fought back to nail Namibia for 161 in 49 overs with captain Paras Khadka, Rahul Vishwakarma and Gyanendra Malla taking two wickets each.
Both Nepal and Namibia are out of the reckoning for the quarter-finals.
In another match that had no bearing on the next round, Bermuda defeated Ireland by 20 runs in group D.
In the last round of league matches on Friday, Pakistan take on Zimbabwe in group A, Australia meet Sri Lanka to decide Group C champions and England clash with Bangladesh for the first place in group D.