Van der Kaay was passed on the swim but had a strong cycle and run to bring the team home for silver.
The New Zealanders clocked 1 hour 22 minutes 27 seconds — 19secs behind winners Germany, with Team Switzerland third in 1:22.35.
Wilde paid tribute to his teammates after the race and sent their potential Olympic Games rivals a warning.
“I think we’ve been racing with each other since 2018 so we know each other inside and out . . . give us another year under our belt and I think we’ll definitely be in the running for a medal,” Wilde said.
“The team carried me today. I had a bit of a low par swim but did good on the bike and the run trying to get us back into contention and we were super lucky to have a strong group with Ainsley. Ainsley did a perfect race with a tactical move and ran brilliantly.”
Germany’s win gave them automatic qualification for the Paris Olympics while New Zealand earned valuable ranking points and are well on track to earning a spot.
It was New Zealand’s first relay medal since the same quartet clinched gold at the world championships in Edmonton in 2019.
The elite individual races were super sprint format — meaning qualifiers, then a three-stage elimination series.
Reid placed eighth in qualifier 1 and Wilde was second in qualifier 2. The top 10 from each advanced to the final. Others went into repechages to decide the other 10 spots for the final.
Wilde was 12th and Reid 13th in stage 1 of the final from which the top 20 progressed.
Tayler was eliminated after placing 11th in stage 2 from which the top 10 moved on to decide the podium placings while Wilde was sixth.
Wilde came into his own in the third stage with a perfectly timed finish in the cycle leg, then a slick transition which earned him precious seconds and a vital margin to stave off Portugal’s Vasco Vilaca and Britain’s Alex Yee by two seconds.
Wilde’s win lifted him to second on the world championship rankings headed by Vilaca. Reid moved up 10 spots to 22nd.
The women’s WTCS race in Hamburg was won by France’s Beaugrand Cassandre by 10 seconds from world championship rankings leader Beth Potter. Van der Kaay was sixth and jumped 11 spots up the rankings to 16th.
The next race of the WTCS is in Sunderland in two weeks.