The Kenyans were up 5-0 until they lost a man to the sin-bin for a high tackle on Curry who was heading to the corner to score.
New Zealand was awarded a penalty try.
Akira Ioane crossed soon after for a 14-5 lead but the Kenyans, who were thrashed 31-7 by Great Britain in their earlier match, continued to frustrate the world No2 side.
Williams was ruled out for the rest of the tournament with the serious injury after he took a crash ball into two defenders early in the second half.
The woes did not end there with Joe Webber dislocating a shoulder in the defeat.
Curry said they were guilty of making too many mistakes.
"Without the ball it's pretty hard to score and when we got it we knocked it on or turned it over at the ruck."
Tietjens said the team's loss against Japan was not for lack of preparation.
"We prepared, we planned. It just wasn't to be, it was just one of those games," he said.
"Japan, to their credit, played very, very well. We made a lot of mistakes. We tended to rush instead of being composed."
Tauranga sailor Sam Meech fared well in his day's races.
In his third of 10 races, he placed fifth and in the fourth race later in the day he was sixth.
He is third overall behind Argentina's Julio Alsogaray and Croatia's Tonic Stipanovic. He races again tomorrow.
In a shock result, the current world champion pairing of Tauranga's Zoe Stevenson and Eve MacFarlane missed a place in the women's double sculls final after they finished fourth in their semifinal yesterday.
Stevenson and MacFarlane missed out by just 0.05sec behind third-placed US.