New Zealand were again in foul trouble - captain Mika Vukona and Frank had two in the opening quarter - and it meant their lead was trimmed to just two points after the first quarter.
But Webster had found his range and when Leon Henry joined the party, the Tall Blacks seemed to have finally found some offensive flow.
The lead reached 18 points and stood at 40-26 by halftime. Defensively, the Kiwis had also held their opponents to six from 27 shots from the field. Suddenly, the huge points differential didn't look so insurmountable and the dream was still alive.
But sustaining such dominance at international level isn't easy and Angola not only scored the first six points in the second half but also landed two more quick three-pointers to close to within three.
New Zealand started to make too many errors - fouls, turnovers and conceded offensive rebounds - and the Angolans were pressing hard and threatening the lead.
But point guard Lindsay Tait stroked a three-pointer, added another basket and snatched a crucial offensive board to make the game safe.
The result meant Group D finished in a three-way tie, but the Tall Blacks' 22-point loss in their opening game proved too much of an obstacle.
New Zealand 68 (Tai Webster 21, Leon Henry 15, Rob Loe 13) Angola 64 (Eduardo Mingas 17, Olimpio Cipriano 11). HT: 40-26.