Alfredo Morelos's sixth goal of the group stage helped Rangers book a place in Monday's draw.
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An 89th-minute equaliser and Ryan Jack's dismissal in added time provided an intense end, but Rangers are through to the UEFA Europa League round of 32 as Group G runners-up.
Alfredo Morelos took advantage of some slack Swiss defending to give the hosts the lead on the half-hour mark and, with Rangers combining well from the outset, they could and perhaps should have been further ahead at the break.
RANGERS v YOUNG BOYS: AS IT HAPPENED
The visitors posed a greater threat in the second half as they chased the game. Out of puff, Rangers began to wilt, while Young Boys' relentless pressing ultimately led to Borna Barišić turning Felix Mambimbi's cross into his own net in the 89th minute to level the scores. For YB, however, it was too little too late.
Alfredo Morelos's first-half goal – his sixth of the group stage – was enough to take Rangers through to the last 32, but nerves were jangling late on. It should have been more comfortable, yet the Light Blues did not take their chances, especially in the first half. Young Boys came into it more in the second period, but for all their possession they created few clear-cut opportunities. Rangers' unbeaten home record in Europe stretches to 16 matches.
Alex O'Henley, Rangers
What it means
- Rangers go through as Group G runners-up, the late equaliser denying them seeding in Monday's draw.
- Young Boys finish third and miss out since Porto's win against Feyenoord means the Portuguese club leapfrog both them and Rangers.
Steven Gerrard, Rangers manager: "I'm not going to stand here and celebrate a draw or finishing second, but let's give credit where it's due. The club's suffered a lot and I think it's the first time it has had knockout football in Europe since 2011. It was about building it back up and this is another push in the right direction, but I won't over-celebrate for sure."
James Tavernier, Rangers captain: "I am delighted that we have got through to the last 32. Having missed out last season and pushed over the line this time – albeit it was hard at the end, but I'm delighted for the club and the boys. They obviously went long in the second half and I think we weren't as tidy in possession as we were first half, so we kept putting more pressure on ourselves. It was disappointing to concede late on, but I can't fault the boys. They put in a hard shift tonight and we're delighted to go through."
Scott Arfield, Rangers midfielder: "The second half wasn't good enough as a whole. The first half was exactly what we wanted to do, to put the pressure on and come out on the front foot. Then Alfredo Morelos gets his goal. The second half was a bit flat and we gave the initiative to them, but given what's at stake then I think the overall picture was to get European football after Christmas and we've done that."
• Morelos has scored 26 goals in 32 appearances in all competitions in 2019/20.
• The Colombian scored for the fifth successive UEFA Europa League game – no Rangers player had previously registered in more than three matches in a row in major European competition.
• Morelos extends his single-season record of European goals for a Scottish club with number 14. The previous record was 12, set by Henrik Larsson in 2002/03.
• Rangers reach the knockout stage for the first time since 2010/11.
• Rangers have won 23 of their 33 matches this season (L3).
• The late own goal was only the second Rangers have only conceded in their last eight home matches.
Rangers: McGregor; Tavernier, Katić, Goldson, Barišić; Kamara, Jack, Arfield; Ayodele-Aribo, Morelos, Kent (Ojo 78)
Young Boys: Von Ballmoos; Janko, Bürgy, Sørensen, Garcia; Fassnacht, Aebischer, Martins Pereira (Mambimbi 73); Moumi Ngamaleu (Spielmann 61), Assalé, Nsame (Hoarau 61)