Alam clipped a ball just wide of Henry Nicholls at short leg, an attempted drive was edged just wide of an outstretched Tom Latham at gully, and one off the gloves fell just short of the cordon.
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.
"We would be unlikely to break up that four-pronged bowling attack," Stead added as another reason why Santner would be competing with Daryl Mitchell for the all-rounder spot.
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.