Bill Demong of the United States was in the lead with just a few hundred metres to go when Stecher, who had been tucked in just behind, suddenly surged clear to win by 5.2 seconds amid heavy snow.
Germany ended up with the bronze medal. World champions Japan performed poorly in the ski jumping session and ended up in sixth.
Austria had endured an indifferent morning session on the ski jump hill which meant they started the 4x5km relay race in third position, 34 seconds behind the second-placed US.
The Austrians quickly made up the difference and the two teams were neck and neck until the end of the third lap, when veteran Felix Gottwald steadily outpaced Johnny Spillane and handed Stecher a 14.1-second lead.
Demong, who won a world title last year, made up the difference and although he overtook Stecher he could not hang on.
"We were hoping to fight for a medal today and we did, it didn't quite go as we wanted at the very end but you can't complain," Spillane, who won silver in the Nordic Combined normal hill event last week, said.
Gottwald won an individual Nordic Combined gold in 2006, when he and Stecher were also in the winning team.
Early last year Gottwald retired and was working as a television commentator when he bumped into a friend who asked him what it would take for him to return to the sport.
The chance meeting prompted Gottwald to end a two year break.
"I tried to answer his question and on the next day in the morning there was still the feeling of coming back," Gottwald, who decided to start training again, said.
"And then at the training the feeling got more intense every day and I just tied to listen to my feeling and not listen too much to my head."
Gottwald, now the most decorated Austrian Olympic winter athlete of all time, has a total of three golds, a silver and three bronzes from three Games.