Dempsey and Dobie cross for Glasgow in opening 20 minutes; Sanele Nohamba halves the deficit in the second half but Fagerson responds for hosts
Horn hits back for Lions, but Horne adds a penalty and Jordan's try further extends Glasgow lead before Brandon claims a late score for visitors
Warriors reach first ever European semi-final
FT: Glasgow 31-21 Lions
That's all from me tonight.
You can read Tom English's match report for that historic victory here.
Thanks for your company - go enjoy the rest of your Easter weekend.
Image source, SNSFT: Glasgow 31-21 Lions
Glasgow head coach Franco Smith has also been giving his thoughts to Sportsound:
"It was an interesting performance in the sense that we didn't have the ball much.
"We looked nervous in attack which is uncommon, but I can understand why - there's a lot of passion and the guys don't want to disappoint. There was a fantastic effort in defence. It's fantastic for the club and I'm pleased to be a part of it.
"[Scarlets] are playing well at the moment. Every game is important now, so we will take things one game at a time."
FT: Glasgow 31-21 Lions
Tom English
BBC Scotland's chief sports writer on Sportsound
Glasgow had to battle for it against a dangerous and physical Lions side.
They won it by 10 points without coming close to delivering the type of performance we know they are capable of.
FT: Glasgow 31-21 Lions
Glasgow scrum-half George Horne on BBC Sportsound:
"They are a physical team and they don't go away, but just chuffed to sneak home at the end there.
"They put us under pressure and held onto ball well. Some of our sets on our own line were outstanding.
"We've put a lot of emphasis on both the league and Europe this year, and we just want to get better every week. We're excited to get into a semi and see what we can do.
"It's a dress rehearsal against Scarlets next week. We want to win every game, so a bit of momentum and a psychological edge would be nice. We know what they can do at home, so it will be tough."
FT: Glasgow 31-21 Lions
Player of the Match Rory Darge has been talking to BT Sport:
"Can't wait for another big game [in the semi-final]," he said.
"We're proud of the effort. They were on our line four times in the first half and didn't score a point.
"It was brutal - they are big boys, and they carry hard, but we stuck to our principles and it was really good to be a part of."
Image source, SNSGlasgow 31-21 Lions
Lions look to finish with a flourish, but they knock-on, and Glasgow are into the Challenge Cup semi-finals, where they will play Scarlets.
Glasgow 31-21 Lions
29 tackles made, peerless at the breakdown, it had to be Rory Darge.
Hamish Watson has a serious challenger for the Scotland seven jersey at the World Cup.
Morne Brandon
Lions refuse to go quietly.
Morne Brandon crashes over from close range, and Gianni Lombard quickly knocks over the conversion.
Glasgow are in absolutely no rush to take the restart.
Tom Jordan
Game over! A first ever European semi-final beckons for Glasgow.
Huw Jones breaks the Lions defensive line, offloads to Ollie Smith, who in turn releases Tom Jordan to score Glasgow's fourth try of the contest.
Over goes the conversion, and the Warriors move past the 30 point mark.
Glasgow 24-14 Lions
Some strong forward carries take Glasgow into the Lions 22.
Another score would kill off this game you feel...
George Horne
Through it goes - nerves of steel!
Glasgow needed that, it halts Lions' momentum somewhat.
Image source, SNSGlasgow 21-14 Lions
Glasgow win a scrum penalty, and George Horne calls for his kicking tee...
Francke Horn
Pure power brings Lions right back into the contest.
Francke Horn takes the ball at pace and smashes his way through several Glasgow defenders on his way to the line.
Over goes the conversion and Glasgow's lead is back to just seven points.
Glasgow 21-7 Lions
For those of you that guessed Rory Darge, well done you.
Glasgow 21-7 Lions
Glasgow win a penalty at the breakdown - I'll give you one guess as to who the man over the ball was.
George Horne roars his delight as the referee's arm goes out in Glasgow's favour.
Glasgow 21-7 Lions
It's all got a wee bit scrappy in the last few minutes.
Franco Smith responds by turning to his bench.
Six changes in one foul swoop - all of Glasgow's replacements are now on. Smith will want them to bring a semblance of control.
Glasgow 21-7 Lions
Lions are attacking again - this is their tenth visit to the Glasgow 22.
Glasgow 21-7 Lions
Lions come forward, but just when they're making real ground, the ball goes to ground and Glasgow have a scrum.
Zander Fagerson
Yes they can!
Glasgow go through the phases, get up to the line, and Zander Fagerson flops over from a yard out.
George Horne continues his perfect record off the tee and restores Glasgow's 14-point cushion.
Glasgow 14-7 Lions
That score seems to have sparked Glasgow back into life.
Richie Gray charges down Sanele Nohamba's attempted box-kick, and then Glasgow steal the resulting lineout.
Can they take advantage?