The Turkish side were 1-0 winners in the away leg, meaning Thursday's result - secured after Ucan opened the scoring nine minutes after his injury-enforced introduction - was enough.
Vladimar Darida brought the Czech League leaders level just after the hour and David Limbersky hit the post in pursuit of a winner that never came.
Both sides started positively, Reto Ziegler shooting wide after two minutes and Marek Bakos forcing the first save of the game when he headed Pavel Horvath's cross at Volkan Demirel.
Plzen mustered another decent break in the 10th minute, winning a corner which Daniel Kolar headed over.
Matus Kozacik , in the away goal, made his first save from Caner Erkin on the quarter-hour - a simple gather from a speculative strike.
Shots were pouring at both ends as the game progressed, though not many were on target. Fener striker Moussa Sow was more culpable than most when he slid one wide from just six yards.
Kolar then missed the target with a second headed effort after half-an-hour's play, Radim Reznik providing the cross on this occasion, and at the other end Sow went close from 12 yards.
The Turks were forced into a change when Mehmet Topal succumbed to injury and Ucan was sent on. It proved fortuitous as the replacement broke the deadlock a minute before the interval.
Cristian Baroni made the pass, Horvath failed to get it clear and Ucan converted from a central position.
Plzen needed to find a way back into the tie but Fener were not willing to make it easy, Dirk Kuyt and Bekir Irtegun both getting shots away inside the first minute of the second half.
Horvath returned fire, waywardly, before Baroni botched a close-range effort that would have put his side in an unassailable lead.
Darida cashed in after 61 minutes, finishing well from Jan Kovarik's cut-back to give the match an added spark.
Eight minutes later the picture almost looked even rosier, but Limbersky's powerful 20-yard attempt cannoned off the upright.
Had it crept inside the post, Plzen would have been ahead on the night and on away goals.
As it was they never went that close again, Kuyt nearer than anyone to scoring a winner in injury-time.