Holding only a narrow 3-2 lead from the home leg, Celta kept their opponents at bay with relative ease for more than an hour before Sisto fired them in front on the night.
Leandro Trossard quickly pulled one back to leave Genk needing only one more to take the overall lead on away goals, but the visitors stood firm to make the last four.
Australia goalkeeper Ryan - on loan from Valencia - played a full game for Genk but saw his Europa League dream ended thanks to Sisto's thunderous strike from the edge of the area.
Celta's away form in Europe this season has been impressive, with wins at Krasnodar, Shakhtar Donetsk and Panathinaikos in their last three away legs.
And they knew it had to be again after conceded twice last week at home to a Genk side who went into this match having kept six clean sheets in eight Europa League home games this term.
Genk had the better of the early exchanges, Mbwana Samatta heading a Trossard cross over and Omar Colley volleying over from inside the area, but Celta were never unduly threatened.
The visitors lost striker John Guidetti to injury in the 42nd minute, Claudio Beauvue coming on in his place, and the substitute was quickly into the action as his right-footed shot from inside the box brought a parry out of Ryan.
Celta ended the first half firmly on the front foot and they started the second in charge too, with Beauvue bringing another save out of Ryan.
At the other end Samatta, who had little joy up front for Genk, with precious little service, saw his shot blocked by defender Andreu Fontas.
Celta broke the deadlock in style in the 63rd minute.
Sisto, the 22-year-old Denmark winger, won the ball in midfield, advanced towards the area and unleashed a fierce effort which flew high into the net.
Genk were not done, though, and four minutes later Trossard brought them level on the night, finding the far bottom corner with a low curling finish from the left of the area.
The tie was back in the balance, but the hosts could not find a winner as Celta booked their place in the semi-finals.