Among the sides to advance on Thursday were Anderlecht, who came from an early goal down against Hammarby to prevail 3-1 on the night and 4-2 over the two legs.
The former UEFA Cup winners, who were beaten in this round by Swedish opposition last term, fell behind less than two minutes in after Paulos Abraham converted a shot from close range.
Hammarby had a couple other opportunities to add onto their advantage, but could not do so. In the second half, the Belgian club sturck via Danylo Sikan to tie the game.
Carrying the game and having the momentum, the hosts got their winner with nine minutes left as substitute Mihajlo Cvetkovic made the most of his chance. Tristan Degreef added a third eight minutes later to complete the victory for Anderlecht.
The loss means that Hammarby are eliminated at the same stage of the Europa League as they were in their only other appearance six years ago.
Next for Anderlecht will be PAOK, who defeated Dynamo Kyiv 2-0. Giannis Konstantelias scored both goals for Dikefalos in a match where the Greek club made the most of their chances. On aggregate, they prevail 5-2.
Dynamo have failed to win any of their last five games on Greek soil since beating PAOK 50 years ago in the European Cup.
The day kicked off with Maccabi Tel Aviv completing their tie against Sheriff Tiraspol, scoring once in Georgia to come out on top 1-0 in their home leg.
Having won the first match 5-0, the Israeli outfit advanced 6-0 on aggregate.
There were two comebacks in the UEL action. One came in Portugal, where Benfica made up for last week's stunning loss against St. Gallen.
Four goals from Vangelis Pavlidis helped them to a 5-0 success and 6-2 aggregate win against their Swiss opponents, who loss Jozo Stanic midway through the second half to a second yellow card.
While St. Gallen conceded six times to Cercle Brugge in the Conference League two years ago, the 5-0 loss was their heaviest in terms of margin of defeat.
The other team to turn things around were Pafos, who overcame their 2-0 first leg reverse to Hajduk Split with a 4-0 victory after extra time.
Hajduk were on the cusp of advancing, but David Goldar netted the leveller in the first minute of second half stoppage time to extend the game. Biel netted what proved to be the winner a few minutes into extra time, while a fourth was added in the final few moments to send Pafos through.
CSKA Sofia take down Qarabag
Perhaps the most significant result on Thursday came in the Bulgarian capital, where CSKA Sofia took Qarabag to penalties after a second 0-0 draw in the tie.
The Bulgarian Cup winners held their nerve in the shootout as they converted all five of their attempts. Matheus Silva was the only player who could not score his spot kick, eliminating Qarabag from the competition.
The Azeris, who are nine-time participants in the UEL group phase, lost a tie in the competition's qualifying rounds for the first time since falling to Eintracht Frankfurt in the playoff round 13 years ago.
CSKA are two rounds away from making it to the main rounds for the first time since 2020/21, when they succesfully negotiated all four rounds of qualification.
Besiktas moved on after getting the better of FC Midtjylland 2-0 on the road. For the second week in a row, the Danes went down a man, making their task more difficult.
It ultimately proved to be their downfall, with the visitors scoring twice in six minutes to complete a 3-0 aggregate win.
Next for Besiktas are Hradec Kralove after the Czech team defeated Tromso 3-1 on the night and 4-1 overall. Despite conceding first, the hosts did not panic, retaking the aggregate lead five minutes later. A pair of goals after the break sealed the deal for them in what was their seventh win in a continental match.
Despite going down a man, Ferencvaros managed to hold off a late Twente comeback. The team from Budapest raced to a two-goal advantage at home, only for their lead in the match to be wiped away in the space of four minutes.
In the end, Twente could not find another goal to force extra time, losing the tie 3-2 on aggregate after the 2-2 stalemate. It was their fourth straight failure in a European two-legged tie.
The third qualifying round will feature the nine winning sides from this stage, 14 eliminated clubs from the Champions League, plus three direct entrants. Winning in that round will secure league phase footall in the fall.
Follow the UEFA Europa League qualifying rounds on Flashscore.