Semak, taking charge of his final Zenit match before Andre Villas-Boas is officially installed as coach on Thursday, saw his reign close with a victory at Signal Iduna Park, although his side failed to turn around their first leg deficit.
Having been beaten 4-2 in St Petersburg, it was Zenit who struck first in the return leg of their last 16 clash on Wednesday, as Hulk registered his fifth of the competition with a wonderful strike from distance to give the visitors hope.
Despite Jose Rondon putting Zenit back in front 17 minutes from time with a stooping header, last year's finalists held out to to mark their 200th match in Europe's premier club competition with progression to the quarter-finals.
After five minutes of the first leg, Dortmund were two goals to the good thanks to efforts from Henrikh Mkhitaryan and Marco Reus, and Pierre-Emerick Aubameyang almost got the hosts off to another flying start in Dortmund as he headed Marcel Schmelzer's cross wide.
Axel Witsel had the game's first effort on target shortly afterwards as the Belgian tested Dortmund goalkeeper Roman Weidenfeller with a long-range drive.
As the Germans responded, Kevin Grosskreutz saw his effort well saved by Malafeev before Sokratis Papastathopoulos headed over from a corner, but for all their possession and forward momentum Dortmund struggled to break down Zenit's resolute back line.
Hulk threatened a repeat of his first-half effort shortly after the break when he sent a free-kick over the crossbar before Viktor Fayzulin's shot drifted wide of Weidenfeller's post.
Rondon's winner may have spoiled the evening for Dortmund somewhat - the Venezuelan arriving to meet a cross from the left - but it changed little as Jurgen Klopp's men followed Bundesliga rivals and European champions Bayern Munich into the last eight.
