Jan Vertonghen gave the hosts an early advantage only for Ruslan Abishov to level.Belgium were carving out plenty of chances, though, and Timmy Simons put them back in front from the penalty spot before Nacer Chadli made it 3-1 at half-time. And Jelle Vossen put the seal on victory with a fourth in the 74th minute.
The win moved Belgium a point clear of third-placed Turkey in the group, with Germany comfortably on course to finish top.
Belgium came flying out of the blocks and Moussa Dembele shot against the bar before Vertonghen opened the scoring in the 11th minute. Simons laid the ball to the Ajax defender who drilled an effort into the bottom corner from 25 yards.
Vossen then had a sight of goal, but fired wide as the hosts continued to threaten, but they were stunned in the 16th minute when Azerbaijan equalised. Abishov headed home Mahir Shukurov's outswinging corner to silence the home fans.
Belgium were back in front on the half-hour mark, though, after Rashad Sadygo's handball in the box and Simons' cool penalty into the bottom corner.
Chadli then went close with a free-kick which goalkeeper Kamran Agayev tipped round the post, and the FC Twente winger did add a third in first-half stoppage time when he headed in Axel Witsel's cross.
Vossen made it four in the 74th minute when he picked out the bottom corner from Eden Hazard's ball in. He nearly gave his side an even more convincing win shortly after but Agayev parried his shot from the edge of the box.