Viergever's late goal in the first leg last week therefore proved crucial as the Dutch outfit came through on aggregate to set up a meeting with Anzhi Makhachkala.
The defender opened the scoring in the return meeting as he escaped the attention of Yevhen Budnik to glance in a header from a corner.
Budnik replied from a corner himself with 18 minutes remaining but Liberec were unable to claim another decisive away goal despite late pressure.
AZ started well, with Nemanja Gudelj and Aron Johannsson having chances before Viergever doubled their advantage in the tie.
Jan Rajnoch brought a save from Esteban Alvarado as Liberec looked for a quick response.
It was not until the second half that the Czechs regularly began to trouble AZ.
They won two corners in quick succession after the break and David Pavelka shot off-target before Esteban saved from Sergiy Rybalka.
Johann Berg Gudmundsson and Viktor Elm had chances for AZ but Liberec gave themselves hope when Budnik tapped in at the back post from a flick-on.
Roy Beerens might have given AZ more breathing space seven minutes from time but his shot was blocked.
Jiri Pimpara, Douglas Djika and Jirri Fleisman all had attempts in the closing minutes as Liberec pressed to the end and there were seven minutes of injury time, but AZ held on.