Guinea international Guirassy became the competition’s outright top scorer with his 10th goal after an hour before turning provider with a fine cross for Pascal Gross to net the second for last season’s runners-up.
Karim Adeyemi struck the third as Dortmund’s rapid counter-attack sliced open the hosts at the Jose Alvalade Stadium.
Sporting controlled the first half but Dortmund stepped up several gears in the second to claim their first win under new coach Niko Kovac, in his second match at the helm.
Dortmund kept their first clean sheet in 14 matches across all competitions as they showed flashes of the quality which saw them stun Europe’s giants last season.
Sporting, who finished 23rd in the group phase and only just avoided the cut, played with confidence and made the early advances.
Rui Borges, appointed in December to replace Ruben Amorim’s struggling successor Joao Pereira, has steadied the ship quickly in Lisbon.
Former Barcelona forward Francisco Trincao’s effort from range was caught by Dortmund goalkeeper Gregor Kobel, and Maxi Araujo’s vicious strike cracked against the crossbar with the stopper beaten.
Kobel used his forearm to keep out a rocket from Conrad Harder, starting up front in place of top scorer Viktor Gyokeres, who was on the bench after a thigh injury.
Young midfielder Joao Simoes was in the right place at the right time to receive a cut-back on the edge of the box, but Kobel saved his shot softly and easily.
Former Bayern Munich coach Kovac’s Dortmund threatened for the first time when winger Jamie Gittens cut in from the left with menace and pinged an effort narrowly wide.
Guirassy missed a golden chance before half-time from close range, but his blushes were spared by the offside flag.
Dortmund, who only just missed out on a top-eight finish and automatic progress to the last 16, came out with far more intent in the second half and claimed their reward.
Rui Silva made a fine save to palm away Adeyemi’s snap-shot, but Gittens had a shot blocked after surging into the area.
Sporting responded by sending on Gyokeres for Harder, aiming to turn the momentum back in their favor.
However, Dortmund took the lead moments later, with Guirassy netting with a superb looping header over Silva from Julian Brandt’s cross.
Nico Schlotterbeck bravely slid in to keep Gyokeres at bay before former Brighton midfielder Gross grabbed Dortmund’s second.
Guirassy produced a superb whipped ball into the danger area from the right, and Gross used his leg to improvise a finish from a few yards out.
With Sporting keen to find a foothold, Dortmund sprung forward on the counter to net their third.
Adeyemi fed Brandt and darted into the box, tapping home when the midfielder put the ball on a plate for him.
It leaves Sporting facing an uphill challenge in the second leg in Dortmund on February 19.
