BVB had goalkeeper Roman Burki to thank for their Tuesday win, after the Swiss made several saves to help the German side qualify for the tournament's knockout stage, reports Xinhua news agency.
Lucien Favre's men took a perfect start on home soil as Sancho continued his scoring run by tapping home the opener after 10 minutes following good work from Marco Reus.
Dortmund gained the upper hand and pressed hard to double their advantage, but Reus failed to extend the lead after losing a one-on-one with goalkeeper Ondrej Kolar five minutes later.
Both keepers had busy nights as Burki had to tip Nicolae Stanciu's one-timer around the post on 20 minutes, and shortly afterwards Reus again went one-on-one with Kolar, with the Slavia goalie again winning that particular battle.
Slavia rallied and leveled the scores before the break when Tomas Soucek finished off a combination move via Milan Skoda in the 43rd minute.
To make things worse for Dortmund, Inter Milan also equalised in their match against Barcelona, meaning the German side would have to better the Ital' result in order to finish Group F ahead of them.
After the restart, Dortmund came out with all guns blazing, knowing that only a win would put them through.
Julian Brandt had a golden chance to give the hosts the lead, but the German international pulled his effort wide six minutes into the half.
Brandt would not be denied on the hour mark, as he slotted home from Sancho's pass to put Dortmund 2-1 ahead.
The latter stages of the game saw Slavia throw everything up front, while Dortmund's Julian Weigl received his marching orders for a second yellow card in the 77th minute, but the German side rode out the storm to win the game and secure their place in the Champions League knockout stages.
With the result, Borussia Dortmund finish second in Group F with 10 points, behind group winners Barcelona (14 points) but ahead of Inter (7 points) and Slavia Prague (2 points).
( With inputs from IANS )