Early goals from Dries Mertens and Timothy Castagne put Belgium 2-0 inside the opening quarter-hour and Romelu Lukaku added a third five minutes into the second half.
Belgium have nine points from their opening three qualifiers, ahead of Russia and Scotland on six points.
Scotland’s hopes of a change of fortunes under new manager Steve Clarke looked dashed after Cyprus equalised late at Hampden Park in Glasgow but Oliver Burke snatched a last-minute winner to seal a 2-1 triumph.
A scorcher from captain Andy Robertson just after the hour mark had Scotland ahead but Cyprus equalised in the 87th minute through Ioannis Kousoulos, only for the Scots to grab back the lead through Burke's header.
Scotland fired Alex McLeish as manager after losing in Kazakhstan and narrowly beating San Marino in their opening two matches of the campaign in March.
Earlier on Saturday, Russia recorded their biggest winning margin as Artem Dzyuba scored four in 9-0 thrashing of San Marino in Saransk, one of last year’s World Cup finals venues.
It took Russia 25 minutes, and the first of two own goals by 20-year Michele Cevoli, to get going but they were 4-0 ahead at halftime.
Dzyuba’s first goal came from the penalty spot and he completed his hat-trick with a follow-up after having a second spot-kick saved. His fourth was the last goal of the one-sided win.
On Tuesday, Kazakhstan host San Marino, Scotland are in Belgium and Cyprus travel to Russia for the next round of group fixtures.
(Reporting by Mark Gleeson; Editing by Ed Osmond)
