Flanker Jerome Kaino and replacement back Beauden Barrett scored tries as defending champions New Zealand battled their way to a 20-18 victory over South Africa in the rain to reach their fourth Rugby World Cup final on yesterday.

Despite dominating most of the possession and territory in a tight, physical game, the All Blacks were forced to endure a nervous last quarter at Twickenham after five penalties from Springbok fly-half Handre Pollard and another kick from his replacement, Patrick Lambie, kept them under pressure until the final whistle.

Fly-half Dan Carter kicked 10 points to complete a deserved victory for the All Blacks, who lifted the Webb Ellis Cup in 1987 and 2011 and were runners-up to the Springboks in 1995. In the final, on 31 October at Twickenham, they will play the winner of today’s second semi-final between Australia and Argentina.

In sharp contrast to their flamboyant 62-13 destruction of France in the quarter-finals, this was a performance of New Zealand forward power and defensive strength. At times, though, South Africa’s relentless physical play threatened to win the day as the All Blacks found themselves repeatedly penalised for indiscipline at the breakdown.

Above all, the All Blacks proved their character in their toughest encounter so far after a largely straightforward run to the last four.

After trailing the Springboks 12-7 at half-time, New Zealand took control of the game in the second half. Their determination to keep alive their hopes of winning the Cup for the first time away from home was clearly on view during the half-time interval.

Carter converted from the touchline to give the All Blacks a 17-12 lead while South Africa lost their prolific try-scorer Bryan Habana to the sin bin for a deliberate knock-on. Pollard replied with a penalty but another kick from Carter kept the All Blacks ahead 20-15 entering the final quarter.