Italy, who had qualified for the finals in Poland and Ukraine last month with two matches to spare, were comfortable winners with two goals for Antonio Cassano and an own goal by Gareth McAuley.
Ending qualification with eight wins and two draws from their 10 games, Cesare Prandelli's rejuvenated Italy will go into the finals as one of the favourites, while Northern Ireland, who end their campaign with nine points, begin the search for a new coach.
Estonia finished second in the group on 16 points to go into the play-offs for the first time.
"We dominated possession and were good enough not to concede," Prandelli, whose Italy side conceded just two goals in a record qualifying group, told Italy state broadcaster Rai.
"The rhythm was excellent and we were aggressive so they never settled on the ball."
Cassano, whose brace took him to nine international goals in 28 appearances, revealed he would quit the Azzurri in three or four years.
"Compliments are nice but they've massacred me enough in the past," the often-criticised 29-year-old Milan striker told Rai.
"Three or maybe four years and then I'll quit. I'll play the Europeans and then maybe a World Cup but then I'll stay with my family and maybe have more children.
"I'm happy but stressed. Football gives you what you put in. Maybe I've given little and that's why I've not won much."
Sebastian Giovinco, who had been handed a place up front after Giampaolo Pazzini and Mario Balotelli had pulled of of the squad injured, almost make the perfect start, combining with Cassano before firing a left-foot shot from 20 metres that skidded hard into Maik Taylor's midriff off the wet surface.
Northern Ireland, who had slipped to fifth in the group following a 2-1 reversal at home to Estonia on Friday, almost fell behind after 19 minutes when Giovinco's spinning corner was flicked on at the near post but Giorgio Chiellini, lunging awkwardly off-balance, could only manage to head wide from point-blank range.
Two minutes later though Italy made the breakthrough when De Rossi lobbed a superb ball over the Irish defence for the run of Cassano who timed his volley to perfection finding the corner for his eighth international goal.
Despite missing a number of regulars including Aaron Hughes and Jonny Evans, Northern Ireland fought back and came close to equalising when Gianluigi Buffon had to throw himself full length to his right to turn aside a Ryan McGivern header.
The home side were enjoying the lion's share of possession though and after Giovinco and Riccardo Montolivo went close, Cassano raced onto an Alberto Aquilani pass after 53 minutes before drilling a low shot into the corner.
After Taylor had turned a Montolivo shot aside he was beaten for a third time in calamitous circumstances after 74 minutes when McAuley kicked the ball from his hands after initially miscuing a clearance.
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