On Saturday, BBC Two failed to show the start of the match in Cardiff, after the channel continued coverage of Andy Murray's semi-final against Rafael Nadal in the ATP World Tour Finals, which had overrun.
The rugby kick-off was made available on the Red Button interactive service and was also shown live on the Welsh-language channel S4C.
However, viewers tuning in to BBC Two missed the first seven minutes of the game, including Stephen Jones's kick which sent Wales into an early lead. The Welsh Rugby Union (WRU) immediately questioned whether the situation would have occurred if England were playing.
Speaking to BBC Radio Wales, WRU group chief executive Roger Lewis said that it was a "schoolboy error" by schedulers, while some viewers had missed out as they did not know how to use the Red Button.
"My concern is this action was symptomatic of an increasing marginalisation of Wales by decision makers in London," he said.
"On this occasion BBC TV bosses in London decided what BBC viewers in Wales could or could not see of a major sporting event taking place in our own country."
Lewis said that the BBC had known well in advance about the kick-off time and therefore could have made contingency plans to accommodate the tennis.
He added: "If someone had put the call in beforehand perhaps we could have pulled this out of the fire."
The BBC apologised to viewers, but said that the tennis was close to its conclusion and the decision was made to stay with the Murray game.
"The Andy Murray versus Rafael Nadal match went on much longer than expected and had reached a pivotal moment, a tie break in the deciding set," said the corporation.
"As such we felt we had to stay with the match to its conclusion. This resulted in viewers missing the first seven minutes of play from the Wales v New Zealand rugby match.
"The match was made available on the Red Button, which was communicated both verbally and visually on screen. We went straight to the rugby the moment the tennis had finished. We apologise if this caused any inconvenience to rugby fans in Wales and elsewhere."