Rangers joined Barca in the last eight despite losing 2-1 at Red Star Belgrade, progressing 3-2 on aggregate.
Qarabag had chances, Tural Baymarov missing from the penalty spot just before the hour mark and Junior hitting the woodwork, but Spurs stayed in control of the match.
Manchester City defeated Brentford 3-0, closing the gap on Premier League leaders Arsenal. Liverpool drew with Chelsea, while other key Premier League results impacted European qualification hopes.
Manchester United captain Wayne Rooney has been left out of the 18-man squad travelling to face Danish side FC Midtjylland in the Europa League on Thursday, the Premier League club said on their website (www.manutd.com). With United fifth in the league table, six points off the top-four, the 30-year-old striker recently said that winning the Europa League or the FA Cup could save their disappointing season. Combative midfielder Marouane Fellaini was another notable absentee and full back Matteo Darmian will not be involved after dislocating his shoulder during Saturday's 2-1 league defeat by Sunderland.
IMAGES from Europa League matches played on Thursday.
Eintracht Frankfurt beat 10-man West Ham United 1-0 in their Europa League semi-final
Lazio, who had won all four previous games, were held to a frustrating scoreless draw by a Bulgarian side who came to defend.
While Spurs play Inter Milan at home in Champions League on Wednesday, on Thursday, Arsenal face a long trip to Ukraine to play Vorskla Poltava in the Europa League, needing a victory to consolidate first place in the group.
Holders Porto will face Premier League leaders Manchester City while former European champions Ajax Amsterdam will meet Manchester United in two glittering Europa League Round-of-32 ties following Friday's draw.
Sunderland defeated Newcastle United 2-1 with a late goal from Brian Brobbey, while Nottingham Forest secured a 3-0 victory over Tottenham Hotspur in Premier League action.
Images from Europa League matches played on Thursday.
United lost 3-2 at home to a fearless and skilful Athletic Bilbao, their second successive European defeat at Old Trafford, in the first leg of their round-of-16 tie. Central defender Xandao scored with a cheeky back-heel to give Sporting a 1-0 win over City in Lisbon, ending the Premier League leaders' run of six straight wins.
Barcelona's women's team showcased their dominance by defeating Real Madrid 6-0, securing a place in the Champions League semifinals. They will face Bayern Munich for a spot in the final.
The 24 sides through from the group phase join the eight third-placed finishers in the Champions League in Monday's draw, including Manchester United and Ajax Amsterdam.
Arsenal cleared arguably the most dangerous remaining obstacle in their path to the Premier League title by the skin of their teeth as Leandro Trossard's late goal secured a dramatic 1-0 win at West Ham United to restore their five-point lead on Sunday.
VfB Stuttgart had to come from two goals down against Norwegian outsiders Molde on Thursday to scrape into the final qualifying round of the Europa League.
Liverpool striker Dirk Kuyt headed a late goal to send the five-times European champions into the last 16 of the Europa League with a 1-0 victory over a defiant Sparta Prague at Anfield on Thursday.
Liverpool diced with elimination before scoring two late goals to win 2-1 at Trabzonspor and squeeze into the Europa League on Thursday while Swiss second division side Lausanne came through with a shock win over Lokomotiv Moscow.
Besiktas's Europa League game at home to Tottenham Hotspur was suspended twice on Thursday after the floodlights failed in each half before the Turkish side won 1-0.
IMAGES from the Europa League matches played on Thursday
Financially troubled Spanish club Real Mallorca have been excluded from this season's European competition by governing body UEFA.
Holders Sevilla swept into a second consecutive Europa League final.
Arsenal moved to the top of the Premier League with a comfortable 3-0 win over Fulham on Saturday, extending their lead in the title race.
'The Europa League is a massive thing for us now -- it's a trophy and it gives us qualification for the Champions League. With the players we have got, we can be unstoppable'
Images from UEFA Europa League semi-finals played on Thursday.
Manchester United secured a dramatic 3-2 Premier League victory over Liverpool, clinching their return to the Champions League after a two-year absence, thanks to a late goal from Kobbie Mainoo.
IMAGES from the Europa League matches played on Thursday
Former European champions Steaua Bucharest and English Premier League Southampton suffered shock defeats by Scandinavian teams in Europa League qualifiers on Thursday.
Arsenal defender Per Mertesacker says the players are focused on winning the Europa League as well as their four remaining Premier League games to give manager Arsene Wenger the perfect send-off.
Alexandre Lacazette's free-kick sent Arsenal into the Europa League semi-finals with a comfortable 1-0 win away over Napoli, while Chelsea beat Slavia Prague 4-3 in a roller-coaster game, helped by a Pedro brace.
Diego Forlan scrambled an early goal to give Atletico Madrid a deserved 1-0 win over a lethargic-looking Liverpool in the first leg of their Europa League semi-final on Thursday.
After a collective blow-out in the Champions League, England has a three-pronged attack on Europe's second tier competition with Chelsea, Tottenham Hotspur and Newcastle United all vying for Europa League success.
Napoli recovered from three goals down to draw 3-3 at Steaua Bucharest in the Europa League on Thursday as holders Atletico Madrid were held 1-1 by Bayer Leverkusen.
AC Milan have been drawn to play Manchester United in what is the standout tie in next month's Europa League round of 16.
West Ham United were knocked out of the Europa League in the third qualifying round on Thursday after a 2-1 defeat at Romanian side Astra Giurgiu.
Javier Saviola and Oscar Cardozo scored two goals apiece and defender Luisao was also on target as Benfica thumped Everton 5-0 in the Europa League on Thursday.
Arsenal's Pierre-Emerick Aubameyang struck a vital late goal to seal a 3-1 win over Valencia on Thursday and give his side breathing space for the second leg of their Europa League semi-final in Spain next week.
Manchester United fans are planning to protest against being asked to pay 71 pounds ($101.5) per ticket for their Europa League away match against Danish league winners Midtjylland on Thursday, according to reports in the British media.
Barcelona will face a struggling Galatasaray team who are 13th in the Turkish top-flight.
The UEFA Cup will be renamed the UEFA Europa League from next season in an effort to boost the competition that has lost much of its appeal, European soccer's governing body said on Friday.