Lukaku's extended his scoring record to 66 goals in his 99th appearance for his country after Belgium were shocked when Estonia captain Matthias Kait stole away the ball in midfield and thundered home a powerful shot to put the home side ahead in the second minute.
But FIFA's top-ranked team fought back to move to 10 points from four group matches while Estonia are bottom after losing their opening three games.
"With the first goal, all credit should go to Estonia," said Belgium coach Roberto Martinez. "It was a great shot. That happens in football. But I'm pleased that we remained calm and the five goals we scored ourselves give satisfaction."
Estonia's dream start lasted 20 minutes before Vanaken equalised with a close-range header from captain Eden Hazard's perfect chip.
The 28-year-old Lukaku put Belgium ahead just before the half-hour mark, using his strength to work a rebound off the defence onto his left foot and into the corner of the net.
He had his back to goal and was given time and space to turn and shoot as he made it 3-1 to Belgium in the 52nd minute.
The goal allowed the visitors to settle into a comfortable rhythm after Estonia had proved more than a handful in the first half and might have had more goals had they been more clinical.
Witsel converted a close range tap-in after 65 minutes when Yannick Carrasco had dribbled his way into the penalty area and the latter was the provider again as Foket scored his first international goal 10 minutes after coming on.
Estonia got a consolation seven minutes from time as Michael Lilander teased his way into the penalty area to provide Sorga with an easy finish to bring the loudest cheer of the night.
Belgium have a much tougher assignment against the Czech Republic in Brussels on Sunday, while Estonia's next qualifier is away to Wales on Wednesday.