Dieter Hecking's side had skipped away to a three-goal lead at the Ghelamco Arena before Gent pulled back two late goals to give themselves a chance in the return bout in Germany in three weeks' time.
The opening goal came in fine fashion when 22-year-old Draxler turned on a dime on the left touchline, played a neat ball into the path of Vieirinha who returned the favour, allowing the Germany international to take a touch before firing beyond Matz Sels from just inside the area.
That saw out the first half before Wolfsburg were quickly at it again when Draxler doubled the lead less than 10 minutes into the second term.
The Wolves ace pounced on an errant backpass from Renato Neto before taking the ball into the area and then producing a deft chip to clear the advancing Sels for his fourth in his past four outings in all competitions.
On the hour-mark, Wolfsburg were three to the good when Christian Trasch was released down the right and provided a perfect ball for Kruse to volley home from close range to give the visitors a commanding lead.
However, Hein Vanhaezebrouck's Gent responded in the 80th minute through skipper Kums who picked up the ball wide out on the left prior to cutting back onto his right foot and firing a bouncing shot beyond fellow Belgian Koen Casteels who only managed to get a hand to the well-placed attempt.
Wolfsburg will now head back to Germany knowing that they have scored three times on the road, making the Volkswagen Arena fixture on March 8 a much more comfortable one than they would have previously thought, however, the two late goals from Gent will be food for thought for Hecking's men.
2015/16 UEFA Champions League - Round of 16 first leg