Philippe Mexes and Simone Perrotta put Roma ahead 2-0 by the 54th minute and the club prevailed for its ninth title to equal Juventus for most Italian Cup crowns.
It was the fourth straight year Roma and Inter have met in the final. Inter won in 2005 and 2006 to increase its title haul to five.
Mexes cut in front of three Inter players to score with a low shot in the 36th minute. It was the Frenchman's second goal of the season with the other coming during league play. Perrotta made it 2-0 in the 54th by tapping in a pass from Mirko Vucinic.
Vitor Hugo Gomes Passos, who came on as a replacement at the beginning of the second half, scored for Inter in the 60th with a hard shot from well outside the area that surprised Roma goalkeeper Alexander Doni.
Gomes Passos scored a similar goal in the Italian Cup semifinals to help Inter through to the final.
After finishing three points behind Inter - which won its third straight Serie A title last weekend, Roma started quickly, creating more chances and dominating the first half at Stadio Olimpico.
It had been 28 years since the Italian Cup was decided in a single game - the last time in 1980 at the same stadium when Roma defeated Torino on penalties.
After cutting Roma's lead, Inter continued pressing and four minutes later defender Nicolas Burdisso hit the post on a header. Roma was rarely dangerous after Burdisso's near miss was forced on the defensive for the remainder of the game.
"My players battled to the end and the result was up for grabs until the last minute," Roma coach Luciano Spalletti said.
The two teams played twice during the season, with Inter winning the first 4-1 in September at the Stadio Olimpico. In February, Roma dominated much of the second game and led 1-0 on a goal by Francesco Totti until Inter captain Javier Zanetti equalized with two minutes remaining.
Inter's Zlatan Ibrahimovic missed the game because of swelling in his knee. The Sweden striker came off the bench after missing six weeks because of the knee injury to score both goals in Inter's victory last week against Parma that sealed the Serie A championship.
Ibrahimovic was to be examined Monday by Sweden's team doctors. The injury is not serious and Ibrahimovic is expected to start training for the European Championship with Sweden later in the week, coach Lars Lagerback said after speaking to the player on Friday.
Inter also was without defender Marco Materazzi and striker Julio Cruz, who scored in the semifinals to earn the team a spot in the final. Both were ineligible because of suspensions. Roma had to do without Totti, who was injured.
Saturday's game might have been the last for Inter coach Roberto Mancini as speculation has persisted that he will be replaced by former Chelsea coach Jose Mourinho.
Mancini has refused to speak publicly since Inter won the title and again would not comment after the loss to Roma.
"We did what we could, but it was a great Roma tonight," Zanetti said. "We are very happy to have won the championship. They won the Italian Cup, we'll see each other next year."
