PSV, who led 2-0 from their home leg, and Belgium's Zulte Waregem both had good chances to take the lead in the first half. The best fell to Eindhoven's Tim Matavz who went one on one with Sammy Bossut before the goalkeeper saved with his foot.
Bossut again did well to thwart Memphis Depay early in the second period after he was played through by Stijn Schaars, but PSV took the lead from the penalty spot in the 56th minute.
A shot from Depay was stopped on the line with his arm by Zulte's Steve Colpaert. Although Matavz put the ball in the net, a penalty was given and Colpaert sent off.
The 1988 European Cup winners added their second through Zakaria Bakkali and Bruno Godeau completed an unhappy night for the Belgian side by scoring an own goal in added time.
Austria Vienna, Zenit St Petersburg and Dinamo Zagreb also survived the third qualifying round but the performance of the night came from Viktoria Plzen who thrashed Estonia's Kalju Nomme 10-2 on aggregate after a 6-2 home win.
Zenit St Petersburg eased through 6-0 on aggregate against last season's surprise Champions League team Nordsjaelland.
Taking a 1-0 lead into the home leg, the Russians scored midway through the first half through Roman Shirokov before Hulk, Danny and Andrey Arshavin added second-period goals.
Shirokov scored his second in added time and Nicolai Stokholm completed a disappointing night for the Danes, who reached the group stage in 2012/13 but won only one point while conceding 22 goals, when he hit the woodwork with a penalty.
Dinamo Zagreb are two games away from reaching the group stages for the third season in a row after earning a 3-0 win against Sheriff Tiraspol in Moldova for a 4-0 aggregate victory.
The Croatians have struggled in the Champions League group stage, losing 11 games in succession before drawing 1-1 with Dynamo Kiev in a snowstorm last December.
Austria Vienna held on with 10 men in Iceland to draw 0-0 with FH and qualify thanks to Daniel Royer's goal from the first leg. Legia Warsaw went through on away goals against Molde after drawing 0-0 in Poland.
Metalist Kharkiv added to the 2-0 advantage they had brought back from Greece when Argentine Sebastian Blanco scored in the second half against PAOK Salonika. PAOK equalised through Tomas Necid but it was too little, too late.
However, the Ukrainian side's first foray in the Champions League could be derailed by a UEFA disciplinary hearing next week, after Metalist lost an appeal over a match-fixing case.
Viktoria Plzen's 38-year-old captain, Pavel Horvath, had a night to remember, scoring a hat-trick in the defeat of Kalju.
The Czechs, leading 4-0 from the first leg in Estonia, were given a shock when Italian Damiano Quintieri opened the scoring for Kalju after 10 minutes. Quintieri scored again in the second half but Plzen were full value for their 10-2 success.
The draw for the playoffs is on Friday. Teams will be divided into a champions group and a non-champions group which includes Arsenal, AC Milan and Schalke.
Five of the 10 teams in each group will be seeded for the two legs on August 20-21 and August 27-28.
Celtic also progressed to the play-offs at the expense of IK Elfsborg after a goalless draw in Sweden.
Champions League third qualifying round results:
FH 0 - 0 Austria Vienna
Zenit Petersburg 5 - 0 FC Nordsjælland
Sheriff Tiraspol 0 - 3 Dinamo Zagreb
Metalist Kharkiv 1 - 1 PAOK Salonika
Elfsborg 0 - 0 Celtic
Viktoria Plzen 6 - 2 Kalju
Legia Warsaw 0 - 0 Molde
Zulte Waregem 0 - 3 PSV Eindhoven