* Roma beat Shakhtar 1-0 to go through on away goals
* Edin Dzeko scores a brilliant 52nd-minute winner
* Roma reach last eight for the first time since 2008
* Visitors have defender Ivan Ordets sent off late on (Adds Dzeko quotes)
ROME, March 13 (Reuters) - A determined AS Roma beat Shakhtar Donetsk 1-0 on Tuesday to reach the Champions League quarter-finals for the first time since 2008 as a magnificent finish by Bosnia striker Edin Dzeko sent them through on away goals.
Roma celebrated only their second win in six meetings with the Ukrainian side and got revenge for a 6-2 aggregate defeat by Shakhtar at the same stage of the competition in 2011.
They endured a nervy finish, however, as Shakhtar ended the match on the front foot despite playing the final few minutes with 10 men after Ivan Ordets was sent off.
Having trailed 2-1 from the first leg, Roma looked bereft of ideas for much of the contest at the Stadio Olimpico before Dzeko broke the deadlock in the 52nd minute following a tepid first half devoid of goal-mouth action.
The Bosnian took a defence-splitting pass from midfielder Kevin Strootman into his stride and beat the offside trap before he steered the ball into the far corner with the outside of his foot past advancing keeper Andriy Pyatov.
The former Manchester City striker, who has been linked with a move back to the Premier League, but said after the match that he did not want to leave Roma, was given a rousing send-off by the home fans when he was substituted in the dying minutes.
"Everyone deserves a standing ovation because we all gave absolutely everything tonight and we fully deserve to be in the quarter-finals," Dzeko was quoted as saying by Sky Sports Italia.
"We achieved something that's been missing for 10 years and are now prepared to face anyone in the last eight. All the other teams are strong but we are strong too."
Shakhtar came close to extending their overall advantage in the 13th minute when Roma defender Alessandro Florenzi headed a floated free kick into the box inches wide of his own far post.
Roma's solitary glimpse of goal in the opening half came in the 28th minute when visiting keeper Pyatov palmed away a fizzing low cross by Aleksandar Kolarov to deny Dzeko a simple tap-in from close range.
The home side came out with renewed purpose in the second half and Dzeko delighted their vocal fans when he broke the deadlock with a trademark clinical finish.
Dzeko also curled a shot from the edge of the penalty area inches wide in the 62nd minute before Shakhtar centre back Ordets was shown a straight red card in the 79th for hauling down the Bosnian when he was through on goal.
Despite being a man down, Shakhtar launched a late onslaught and had several dangerous raids down the left flank but the home team's defence held on until the final whistle.
Roma's former captain Francesco Totti, who watched anxiously from the terraces, was overjoyed at fulltime.
"A fantastic result, a fantastic Roma," he said on the club's official twitter account. "Among the eight best sides in Europe and we push onto the next round." (Writing by Zoran Milosavljevic; Editing by Toby Davis)