The Dutch giants were held to a 2-2 in the first leg in Belgium, but had no such problems in this game.
The scoring was opened when their veteran striker Huntelaar slotted home in the 30th minute, to score his fourth goal in as many games.
Only four minutes later centre-back Matthijs de Ligt headed home a corner to double Ajax's lead.
Just after the break, David Neres secured the team's place in the final round of qualification following an assist from ex-Southampton player Dusan Tadic.
The Amsterdam-based team will now go on to play Dynamo Kiev for a place in the group stages of Europe's biggest club competition.