Leslie (19), who trains at the Naseby Luge Track in the New Zealand winter, took the placing in Winterleiten, Austria, in a field of 34, New Zealand Luge Association president Geoff Balme said.
Leslie had only just missed out on second after a close race, Balme said.
''Second in the first heat, Leslie was on track for the fastest time in the second heat when his sled went over some sort of obstruction, possibly a stone or a piece fallen from another sled, which damaged the edge of his runner and slowed him through the lower section of the track, relegating him to third place.
He ended the race one second out of first place and 2/100ths of a second out of second place.''
The event was won by Austrian Fabian Achenrainer from compatriot Florian Markt in second.
It was the first of four races planned for the northern hemisphere winter, Balme said.
Leslie, who won the overall junior world cup title in the same event last year and was second at the junior world championships, said he planned to compete in senior events this year as well as focusing on the junior world cup.
Balme said Leslie had ''picked up where he left off at the end of last season, so this boded well for this season''.
