Ramsey rubber-stamps Arsenal progress
Leading 3-0 from last week's first leg, in which Ramsey also scored, Arsene Wenger's men finished the job in unfussy fashion at the Emirates Stadium thanks to a goal in each half from the in-form Welsh midfielder.
It was a third straight victory for Arsenal since the shock of their 3-1 loss to Aston Villa on the opening day of the Premier League season, but an injury to Lukas Podolski took some of the gloss off the evening.
The German appeared to succumb to a hamstring injury early in the second half, which will only increase calls from impatient fans for Wenger to add new players to his squad in the final days of the transfer window.
The first-leg result meant Fenerbahce had not travelled in hope, and they must now await the Court of Arbitration for Sport's decision on their appeal against a two-year UEFA ban for match-fixing, which will be delivered on Wednesday.
Arsenal had an early fright when Raul Meireles deflected Bacary Sagna's attempted clearance back towards goal and Wojciech Szczesny had to produce a reflex save, but the tie was wrapped up inside 25 minutes.
Podolski sent Theo Walcott into the Fenerbahce box and although he was dispossessed, Caner Erkin's sliding challenge sent the ball straight to Ramsey, who swept home from 12 yards.
Fenerbahce goalkeeper Volkan Demirel prevented Olivier Giroud from increasing Arsenal's advantage with a sharp save, before Szczesny displayed his alertness at the other end by touching Emmanuel Emenike's drive onto the post.
The aggregate scoreline robbed the game of any real drama, but there was a moment of potential significance early in the second period when Podolski had to be stretchered off with what looked to be a hamstring problem.
Wenger can scarcely afford to lose more first-team players, and the appearance of sole close-season signing Yaya Sanogo from the bench only served to highlight his lack of options in the forward line.
There was solace, of sorts, on the pitch, however.
Demirel produced a finger-tip save to deny Santi Cazorla and Walcott bent a free-kick against the crossbar, before Ramsey made it 2-0 in the 72nd minute with an insouciant side-foot volley from Kieran Gibbs's cross.
Ramsey walked off the pitch and onto the substitutes' bench before injury time had elapsed, without being replaced, but there was no indication that he, too, had succumbed to injury.
Related Arsenal News