Just four minutes later, Belgium came within a whisker of opening the scoring as Eden Hazard played in Kevin De Bruyne, who swivelled before firing towards the bottom corner, but goalkeeper Anastasios Kissas was on hand to make a smart save.
The Red Devils were dominant in the opening stages and duly took the lead 21 minutes in as Christian Benteke and Witsel kept the ball on the edge of the box before laying it off to Fellaini, who turned well and lashed home.
Cyprus simply could not contain Belgium and it would not be long before they conceded a second goal, with Hazard's cross in the 35th minute falling perfectly to Benteke, who made no mistake to nod into the net from close range.
Belgium picked up from where they left off after the restart, but their opponents were able to hold off the Red Devils until past the hour by dropping deep and defending stoutly.
The hosts would breach Cyprus's defence once again, however, as Fellaini struck his second of the night in the 66th minute thanks to a vicious curling effort from outside the area that rippled the top corner of the net.
No sooner had the visitors kicked off that they found themselves four goals down, with Hazard collecting the ball outside the box before weaving past two defenders and firing home.
Belgium then added a fifth in the 80th minute when substitute Michy Batshuayi grabbed a debut goal with a neat finish from just inside the box.