Phillip Cocu's men made hard work of a 2-0 home victory over the plucky Belgians in last week's first leg and tonight's hosts gave little away until Steve Colpaert was sent off in the 56th minute.
Tim Matavz scored the resulting penalty and the Dutchmen soon forged ahead to capitalise on their one-man advantage, with Zakaria Bakkali notching in the 73nd minute before Bruno Godeau put through his own net on the stroke of full-time.
Zenit St Petersburg were another side who made no mistake in booking their place in the play-offs by thrashing FC Nordsjaelland 6-0 on aggregate.
The Russians had only edged a slender 1-0 win in the first leg but quickly dispelled any hopes there were among the travelling Danish fans of taking a seeded scalp.
Roman Shirokov opened the scoring on 26 minutes before Hulk (50) and Danny (62) struck after the break to give Zenit an imposing lead.
Substitute Andrey Arshavin added a fourth goal in the 68th minute and the hosts even rode out the dismissal of defender Luis Neto to complete the rout through Shirokov on the stroke of full-time.
Viktoria Plzen shared an eight-goal thriller with Nomme Kalju which saw the Czech side emerge 10-2 aggregate winners when the dust finally settled.
The Estonians were never likely to overturn a 4-0 first-leg deficit but they could not have predicted the scoreline in Plzen - despite opening the scoring through Damiano Quinteri in the 10th minute.
Pavel Horvath soon scored a 20th-minute penalty and added a second goal just before half-time with Stanislav Tecl making it 3-1 in the 58th minute. That was Horvath's cue to complete his hat-trick on 62 minutes but Quinteri would manage to score again seven minutes later.
Plzen brushed off any thoughts of a Kalju comeback, however, as late goals from substitutes Tomas Horava (71) and Tomas Wagner (82) rounded out a 6-2 win on the night.
Dinamo Zagreb ensured Croatia were represented in the next round after cruising to a 4-0 aggregate win at Sheriff Tiraspol of Moldova.
Dinamo led 1-0 from the first leg and goals from Said Husejinovic (10), El Arbi Hillel Soudani (27) and Duje Cop (61) put the outcome of the tie beyond doubt.
Elsewhere, Austria Vienna survived the second-half dismissal of Markus Suttner to ride out a goalless draw at FH Hafnarfjordur and progress with a 1-0 aggregate victory, while a 1-1 draw between Metalist Kharkiv and PAOK was enough to see the Ukrainian club progress.
Metalist held a 2-0 advantage before tonight's game and Sebastian Blanco effectively poured cold water on Greek hopes of a comeback with a 72nd-minute goal, but substitute Tomas Necid would pull one back seven minutes from time.
A goalless draw against Elfsborg in Boras was enough to give Scottish champions Celtic a 1-0 aggregate win and Legia Warsaw progressed on away goals after holding 10-man Molde to a stalemate in Poland following last week's 1-1 draw. Emmanuel Ekpo received his marching orders for Ole Gunnar Solskjaer's side.
The 14 clubs who have been successful in the third round can now look forward to being drawn against seeds Arsenal, AC Milan and Schalke while non-seeded clubs Pacos de Ferreira and Real Sociedad also enter the mix.
Basle, Steaua Bucharest, Maribor, Shakhter Karagandy, Fenerbahce, Ludogorets and Lyon are the other clubs who have qualified for Friday's draw in Nyon.