With the scores goalless after the first leg of the last-32 tie, BATE's hopes of progressing were hit by the dismissal of Dmitri Baga.
And Cristian's spot-kick before the interval was enough to see Fener scrape through to a meeting with Viktoria Plzen.
Thursday night's second leg was played behind closed doors at the Sukru Saracoglu Stadium after the Turkish club were penalised by UEFA over missiles being thrown by supporters during December's home group stage fixture against Borussia Monchengladbach.
Despite the unfamiliar atmosphere, Fenerbahce took just five minutes to produce their first chance with a left-footed drive from Cristian which flew past the right post.
Salih Ucan then found himself in space soon after but failed to connect properly with the ball, allowing BATE goalkeeper Andrey Gorbunov to gather with ease.
BATE had yet to register a shot on goal and their task was made all the more difficult by a red card for Baga after 21 minutes, with the midfielder booked twice in quick succession for fouls on Dirk Kuyt and Ucan.
Fener were soon in control and Gorbunov had to be at his best in pushing away Pierre Webo's 12-yard strike at full stretch.
Gorbunov had been the busier of the two goalkeepers so far but his hard work was undone on the stroke of half-time when he conceded a penalty for a trip on Moussa Sow, with Cristian planting the spot-kick into the bottom right corner.
Fener pressed from the whistle in the second half with both Filipp Rudik and Sow forcing saves from Gorbunov.
Cristian was also unlucky to hit the bar from an angle after 52 minutes and the Brazilian continued to cause problems, with his free-kick shortly after the hour headed over by Sow.
BATE had some respite after 70 minutes with a break down the other end but the finish from Alexander Yurevich was poor and easily held by Volkan Demirel in the home goal.
Ilya Aleksievich and Egor Filipenko also saw chances come to nothing as the away team applied some late pressure.
Aleksievich then gave it once last try for BATE with a right-footed volley from distance but defender Egeman Korkmaz cleared the danger as Fener clung on.