With their season on the line, Arsenal produced a devastating first-half performance to beat Slavia Prague 4-0 in the Czech Republic and reach the Europa League semifinals.
They'll meet a familiar face there - former manager Unai Emery, who also guided Villarreal into the last four on Thursday with a 2-1 win over Dinamo Zagreb.
The other semi-final will see Manchester United, who beat Spain's Granada 2-0 with Edinson Cavani scoring his 50th European goal, take on Italian side Roma, who drew 1-1 with Dutch side Ajax to squeeze through 3-2 on aggregate.
Arsenal's win in the Czech capital - secured courtesy of a three-goal burst in six minutes from the 18th minute - clinched a 5-1 aggregate victory to set up the reunion with Emery.
The Spanish coach spent an underwhelming 18 months at Arsenal as Arsene Wenger's replacement in 2018-19 and is rebuilding his managerial career at Villarreal, who have advanced 3-1 on aggregate against Zagreb.
Fellow Premier League team Man United are back in the last four for a second straight season after completing their 4-0 aggregate win.
Arsenal and Roma were under pressure to advance because the Europa League represents their only chance of winning a trophy this season and their only realistic route into next season's Champions League, owing to their lowly current placing in their domestic leagues.
The winners of the Europa League earn an automatic spot in the far more lucrative Champions League.
Arsenal scored three times in quick succession, first though Nicolas Pepe in the 18th and then Alexandre Lacazette - from the penalty spot - and Bukayo Saka.
Lacazette, continuing as striker with Pierre-Emerick Aubameyang sidelined after contracting malaria, added a fourth in the 77th minute.
Villarreal's goals were scored by Paco Alcacer and Gerard Moreno at the end of the first half, with Zagreb - the last-16 conquerors of Tottenham - grabbing a consolation through Mislav Orsic.
Edinson Cavani's milestone goal was the highlight of United's win at Old Trafford, the 34-year-old Uruguay striker meeting a flicked header back into the middle of the area by Paul Pogba with a left-foot volley into the bottom corner in the sixth minute.
A 90th-minute own-goal by Jesus Vallejo completed a second straight 2-0 win over Granada.
Roma will look to inflict another last-four loss on United after surviving a scare against Ajax, who took the lead through Brian Brobbey's lob in the 49th to tie the score on aggregate at 2-2.
Edin Dzeko equalised in the 72nd and Ajax couldn't find the goal that would have taken the match to extra time.