The team had went into the game full of confidence after defeating the South Africans earlier in the competition.
The silver means Team NI's wait for gold continues.
In the final at Kelvingrove Neil Booth, playing alongside Paul Daly and Neil Mulholland, went down to a 19-10 defeat as Bobby Donnelly, Prince Nelounde and Petrus Breitenbach collected the Rainbow Nation's sixth gold of Glasgow 2014.
Northern Ireland had already taken care of rivals Scotland and Wales on their way to the gold-medal match.
But they were under pressure as soon as the South Africans picked up 11 shots in the space of seven ends to surge 14-3 ahead.
Booth's men responded with seven shots in three ends to raise faint hopes of a comeback, but a double for South Africa in the 15th exchange put them back on course for victory.
The silver is a first Commonwealth medal for Daly and Mulholland but a fourth in five Games for Booth, a second silver to add to a gold and bronze. He still has one more chance to add to that collection in the fours this week.
"You're always disappointed with silver or bronze but we can be very proud and hold our head high," Booth said after the game.
"We still have fours to go and can end on a high. I was telling the boys, 'It's the last time I'll play at a quarter to nine on a Monday morning'."
Daly, in his second Games after appearing in Delhi four years ago, commented: "We're disappointed not to have won the gold but looking back a silver medal is a great achievement for all the games we've got through and all the opponents we've beaten and all the games we've come from behind, it's fantastic to win the silver."
Mulholland on his making his Games debut, added: "I couldn't have asked for any better. The objective coming over was to get a medal and see what colour it would be if we were to get that far. We couldn't send Neil out with a gold but maybe it will come in the fours."
Sports Minister Carál Ní Chuilín has congratulated the team on their win.
She said: "While the bowlers will be disappointed in losing out to South Africa in the final, they can be proud of their achievements this week and their hard work in preparing for the games has been justly rewarded with a silver medal.
"It's a fantastic achievement and I congratulate the trio on their success," said the Sinn Féin minister.
Chief Executive of Sport Northern Ireland, Antoinette McKeown, has also congratulated the bowlers.
She said: "I am delighted for the Men's Triples on winning a Silver medal at the Commonwealth Games.
"Our athletes have once again done us proud shining on the global stage at the Commonwealth Games in Glasgow - proving to be ambassadors for their sport, their communities and themselves