Goals either side of half time from Napoli's Dries Mertens and Nacer Chadli of West Bromwich Albion were enough to see off the Eastern European minnows and secure maximum points for Roberto Martinez's side.
The Red Devils almost took the lead in the 12th minute when Chadli shook off his marker and went for goal from the edge of the box, his effort went sailing just wide.
The hosts offered little in the final third and their hopes of causing an upset were dealt another blow just before half time when Artjom Dmitrijev was shown a red card for a dangerous tackle on Marouane Fellaini.
Aksalu atoned for his first-half blooper with a string of saves in the second period as Belgium piled on the pressure, but he was left helpless three minutes from time when De Bruyne's through-ball picked out Chadli so the West Brom man could stroke the ball home from close range.
The result sees Belgium extend their lead at the top of Group H over second-placed Greece to five points, with both sides having played six games.