Anichebe came on in the 75th minute and earned a penalty seven minutes later which was calmly converted by Arteta.
The 19-year-old sub then ended a strong run with the right finish from close range in the 88th minute to give the Toffees their second win in as many group stage matches.
Boss David Moyes made one change from the team that defeated Birmingham 3-1 in the Barclays Premier League last weekend.
Alan Stubbs was missing with a hamstring injury, so Joleon Lescott took his place in central defence and Nuno Valente started at left-back.
• Moyes hails sweet win for Toffees
Andrew Johnson (ankle) and James Vaughan (thigh) had not travelled to Nurnberg, who were forced to replace the injured attacking duo of Angelos Charisteas (ankle) and Robert Vittek (knee).
The visitors almost grabbed a dream start as they hit the post after just 20 seconds.
The inspirational Arteta found himself with space on the right channel, forcing Jaromir Blazek into a spectacular one-handed save with his shot from 18 yards out.
The rebound landed to the feet of Tim Cahill, whose close-range effort was deflected against the left post.
Nurnberg's Ivan Saenko tried his luck from 25 yards, before a blunder from Lescott almost let the striker in again - but Tim Howard rushed out of his goal to avert trouble.
After Marek Mintal and Dominik Reinhardt misfired from long range, Everton launched another promising attack.
Leon Osman was put in the clear inside the right penalty area and delivered a superb pass to the middle - only for the ball to just evade Cahill, sliding in at the far post.
Peer Kluge almost gave the Germans in the lead when he rammed a powerful shot inches wide from 20 yards out.
Seven minutes later, on the half-hour mark, Reinhardt shot goalwards from an almost identical position on the right - but Howard did well to keep his effort out.
Nurnberg4s defence continued to look shaky at times and they were exposed again in the 37th minute when Arteta and Cahill worked a tidy one-two combination with the 25-year-old Spaniard hitting the wrong side of the post with a shot which hit his team-mate's chest.
Only three minutes later, confusion reigned again in Nurnberg4s box, with Ayegbeni Yakubu eventually steering the ball goalwards from six yards out - but Blazek was quick to react and jump on the weak attempt.
Three minutes into the second half, Mintal was denied by Howard, before Yakubu won a free-kick some 30 yards in front of the Nurnberg goal - but Arteta4s deflected shot went narrowly over.
The classy Spaniard almost caught Blazek napping just four minutes later.
After outfoxing two defenders on the right wing, he surprisingly shot left-footed from the edge of the penalty box - and the Nurnberg goalkeeper needed two attempts to control the ball.
Even though the Toffees seemed to hold the upper hand, Nurnberg got closer to scoring as Kluge proved unable to control a right-wing ball which would have sent him clear.
With 15 minutes to go, Moyes took off Yakubu and brought on Anichebe - a move which was to prove crucial.
Less than eight minutes later he had been brought down in the box by Glauber, who was booked, and Arteta held his nerve to calmly beat Blazek with a shot to the top left corner.
Anichebe then crowned a spectacular cameo performance in the 88th minute when he stormed into the box from the right wing, evaded a challenge and beat Blazek with a low shot from a tight angle.
Moyes hails sweet win for ToffeesDavid Moyes hailed Everton's controlled performance as well as reserving praise for Victor Anichebe after the 19-year old inspired the Toffees to a late 2-0 victory at Nurnberg.
The Nigerian-born striker came on in the 75th minute and used his lightning
speed to earn a penalty eight minutes later when Leandro Glauber wrestled him
down in the box.
Mikel Arteta fired the Toffees into the lead before Anichebe put a clinical
finish on another superb run into the box to knock the ball home from close
range to double the lead with two minutes remaining.
'It was a great start for us and I hope we can go on and qualify,' Moyes
said after the second win in as many group matches. 'I am very pleased with our
performance.
'This was a proper European night in a great stadium. I think we have done
very well. We came here and controlled most of the game.'
The Merseysiders almost took the lead after 20 seconds but Arteta had his shot
saved and Tim Cahill could only hit the post on the rebound.
'We got off to a good start and I could not believe we had almost scored
after 30 seconds. Sometimes when you don4t score you just think `It4s one of
those nights' but I was waiting for the goal to come,' Moyes added.
Arteta insisted the Toffees were always in control, telling PA Sport: 'We
had the best chance of the game in the first minute. After that there was not
much happening and we controlled the game well. We had to wait because they are
a good passing team so we had to wait for the right moment and we had Victor to
change the game.'
Moyes also hailed Anichebe for his late heroics.
'Victor really had a big impact on the game,' Moyes continued. 'He has been
suffering from a broken hand. That4s why I kept him on the bench because I was
not sure where he was. He has not trained a lot but he is a great talent. He
came on and did really well. He has been great for us.'
Moyes also thanked the thousands of Everton fans in the stands who made almost
as much noise as the home fans.
'The support has been unbelievable,' he said. 'Our fans have been waiting
for this a long time. You can see by the support how much they have been longing
for it. There was no motivational speech needed tonight. The support was
fantastic. They want us to do well and had a big impact on the game.'
Nurnberg boss Hans Meyer was furious after the final whistle claiming the
defeat had been self-inflicted.
'This was a self-made loss,' he raged. 'I can4t believe we put our slowest
man, Glauber, against one of the fastest players in England.
'Shall I now beat the hell out of Glauber because he was too slow to keep up
with his opponent? No. I think we played very well but we lacked discipline and
got confused after their substitutions. That is very annoying.'
Nurnberg 0 - 2 Everton
