It took Rizwan just 60 deliveries to bring up his sixth half-century, fittingly reaching the mark with a boundary to underscore his aggressive approach despite the green wicket.
Alam had been discarded by Pakistan in 2009 after three Tests and a best innings of 168, and since his recall this year his highest score was 21 against England in August.
Azhar Ali was caught behind off an outswinger for five, and although the umpire initially said not out New Zealand sought a review which proved otherwise.
The top five West Indies batsmen totalled only 267 across their four Test innings, just 16 more than New Zealand maestro Williamson scored on his own in the first Test.