The Royals keeper, who had made some fine saves earlier in the match,
allowed Alexis Sanchez's low shot to squirm between his legs and over
the line on 115 minutes, which was enough to see the Gunners return to
Wembley on May 30 to try to defend the trophy.
Sanchez had swept the Gunners into the lead on 39 minutes.
However,
Reading were level when Garath McCleary's volley was deflected past
goalkeeper Wojciech Szczesny, who could only palm the ball back over the
line.
Arsenal twice hit the woodwork through a header from
defender Gabriel and a close-range shot by Aaron Ramsey, but could not
find a winner in normal time.
Arsenal manager Arsene Wenger named a
strong XI and made the expected positive start, with Danny Welbeck the
main outlet as he latched onto a through ball into the Reading penalty
area from full-back Kieran Gibbs, which goalkeeper Federici came out to
block.
The Royals number one had to be alert again with a smart
save on eight minutes when Per Mertesacker met a corner from Mesut Ozil
at the near post.
Reading - who had lost all off their past 12
meetings with Arsenal over the past 80 years - looked to counter
themselves and had plenty of pace through Scotland forward Jamie Mackie.
Midfielder Jordan Obita tested Szczesny, back in goal for the cup tie on his 25th birthday, with a low effort from 25 yards.
Sanchez
darted clear and stabbed the ball past the advancing Federici, before
being clipped by the goalkeeper's trailing leg well outside the penalty
area. However, referee Martin Atkinson signalled only for a goal-kick.
Reading
- who had conceded just two goals in their five FA Cup ties this
season, but were without a victory in six league games - sat deep as
Arsenal failed to break them down.
The Championship side, though, were finally carved open on 39 minutes by a goal of the highest craftsmanship.
Mesut Ozil looked up, some 30 yards out, before floating a perfectly weighted pass to Sanchez in the penalty area.
The diminutive Chile forward turned back inside Garath McCleary before slotting past Federici.
With the pressure eased for the second half, Arsenal started brightly, as a backward header from Mertesacker dropped just wide.
Reading looked in need of something extraordinary to revive hopes of making a first FA Cup final in the club's history.