With a 4-2 away win in the bank, Borussia held almost all of the cards and played them conservatively to secure their passage even as they lost 2-1 on home soil.
Hulk's 16th-minute wonder-strike for Zenit was cancelled out by Sebastian Kehl seven minutes before half-time, and although Zenit substitute Rondon scored a second with 17 minutes to go, there was little threat of them getting back on level terms.
The only significant negative for Jurgen Klopp was a yellow card for his striker Robert Lewandowski, ruling him out of their next match.
It should have been even easier for Dortmund, but they wasted perhaps the best chance of the night five minutes in when Pierre-Emerick Aubameyang reached a near-post cross unmarked, only to head inexplicably wide.
Zenit had threatened with a decent effort from Axel Witsel, gathered at the second attempt by Roman Weidenfeller, but when their breakthrough came, it came out of nothing as Hulk, with his back to goal 30 yards out, spun away from his man and then hit a fierce shot into the top left-hand corner.
Kehl then broke into the area to connect with Marcel Schmelzer's cross, heading it down into the ground as Viacheslav Malafeev tried in vain to keep it out.
Dortmund shut the game down in the second half. With the play taking place in near slow-motion, Rondon was able to slip past Mats Hummels to head in a second for the visitors but, other than a late, dangerous cross from Hulk which eluded his team-mates, there was no sign of Zenit comeback.
Meanwhile, Jose Mourinho, the Chelsea manager, has been charged with improper conduct by the Football Association after going on to the pitch during the defeat at Aston Villa on Saturday. Mourinho was sent to the stands by referee Chris Foy after encroaching following a red card shown to Ramires. He has until March 24 to respond.