Postpublished at 22:16 British Summer Time 15 August 2017
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Live coverage on BBC Radio 5 live and online
Uth strike gives Hoffenheim hope for second leg
Milner cross loops in off Nordtveit deflection after Alexander-Arnold scores free-kick
Mignolet saves Kramaric penalty after Lovren foul on Gnabry
Second leg on Weds, 23 August - winner reaches group stage
Get involved #bbcfootball
Gary Rose
Still reading this? What are you playing at!? Get MOTD rewind watched. It's on the Red Button and online here.
That's it from us, I'll leave you with Des.
Cheerio.
Everyone loves European football under the lights at Anfield. The second leg takes place next Wednesday at 19:45 BST.
Tomorrow it's Celtic's turn to take a first step towards sealing a place in the Champions League group stages. They host FC Astana at 19:45 BST.
Hoffenheim's head of international relations and scouting Lutz Pfannenstiel has been reacting on 5 live.
"We've played against Bayern and Borussia Dortmund and now to go to Anfield it is something new for our players.
"Maybe they will be nervous or maybe they will grow wings and fly. It was a cracking goal and it keeps us alive. We showed we can play decent football and Liverpool showed they can kill you with two or three key movements."
Hoffenheim 1-2 Liverpool
Liverpool boss Jurgen Klopp, speaking to BT Sport: "Hoffenheim had a specific plan to play. We gambled a little too much on the wing, it was a little dangerous in the first half, but as always when we play football, we found spaces in-between and created wonderful chances.
"The result is OK. The first half is done and if you said before the game we would win, I would take the result.
"We need Anfield, what an intense game for both sides. I am looking forward to a European night at Anfield. Only the person who does not know about Hoffenheim can be surprised by this."
Hoffenheim 1-2 Liverpool
Mark Lawrenson
Former Liverpool defender on BBC Radio 5 live
Liverpool made better chances. Hoffenheim missed that penalty which was an absolutely pathetic penalty miss. Liverpool will always give you chances and I think every team will look at them and think 'we can beat them'.
If you look at Matip and Lovren they're not great organisers. They rarely communicate.
There's a treat for you coming up at 22:00 BST.
Watch the first MOTD of the Premier League era on the Red Button and online.
Great bit of nostalgia. The Hoffenheim boss was only five years old!
Hoffenheim 1-2 Liverpool
Liverpool's free-kick goalscorer Trent Alexander-Arnold on BT Sport: "It's a thing of dreams to make your European debut for your boyhood club and especially to mark it with a goal. We're disappointed with the late goal but it's good to take a lead back to Anfield.
"I got egged on to take the free-kick. I had the confidence to finally take it. We know it won't be an easy game but we have strategies to beat them."
Hoffenheim 1-2 Liverpool
More from Jordan Henderson: "Trent is brilliant. He was outstanding last season and he has come back and gone up a level in pre-season.
"The free-kick is no coincidence he has been doing them every day in training, that is why he is on them."
Hoffenheim 1-2 Liverpool
Liverpool captain Jordan Henderson on BT Sport: "We're disappointed with the goal we conceded but overall we have to be pleased with the result and how we played at times, we looked dangerous on the attack.
"We knew this would be a tough game, Hoffenheim are a very strong team. Si made a great save from the penalty but then we grew in confidence."
Jbin Matthew George: Scrappy win. Not convinced by Salah though. Quick yes, but his touches, especially with his weaker foot need a lot of work.
Toria: Bit frustrating not to keep a clean sheet but so relieved and 2-1 is something we can work with.
Hoffenheim 1-2 Liverpool
Chris Waddle
Ex-Spurs and England winger on 5 live Sport
Liverpool were the better side and they could have put the game to bed. Hoffenheim will think they have a chance though.
I'd be very shocked if Liverpool didn't win and go through.
BBC Radio 5 live
Straight up at 22:00 BST on 5 live you can listen to the Football Social.
Join in the conversation and give your reaction to Liverpool's result, the cash Everton are about to splash on Gylfi Sigurdsson and anything else that floats your boat.
Plus, Chris Waddle and Mark Lawrenson give their all-time Premier League XIs.
Call 08085 909 693 or text 85058 to get involved.
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Javel Bleach: Score should be 5-3 to Hoff. Easiest opponent #Liverpool, external will have in Europe this season, assuming they finish the job.
Andrew Ogley: Ok ... sell Coutinho for as much as we can get and buy a new defence ... this has been awful to watch
Hoffenheim 1-2 Liverpool
That's it. Liverpool take the win and the two away goals.
It was nervy at the end, but that's a great result for Jurgen Klopp's side.
The late goal for Hoffenheim, meanwhile, keeps them just about it in it.
Hoffenheim 1-2 Liverpool
Oh massive chance!
Kerem Demirbay's deliver is pinpoint and Benjamin Hubner rises unchallenged inside the box. It's a free header, six yards from goal but he plants it high over the bar.
Hoffenheim 1-2 Liverpool
Four minutes go up on the fourth official's board and the home fans roar encouragement for their players.
A free-kick now for Hoffenheim...
Hoffenheim 1-2 Liverpool
Hoffenheim are pressing now.
Liverpool have a couple of away goals but to concede another would be hugely frustrating. The Reds have three minutes to keep their concentration.
Meanwhile , Marko Grujic is on for Sadio Mane for Liverpool.
Hoffenheim 1-2 Liverpool
Chris Waddle
Ex-Spurs and England winger on 5 live Sport
It's from the diagonal ball. It's usually Moreno that's been caught out by the diagonal ball but this time it was Alexander-Arnold.
Mark Uth
Hoffenheim grab a potentially crucial goal as Liverpool switch off at the back,.
Dejan Lovren plays Mark Uth onside as a long ball from the back is sent into the area and Uth chests it down before sweeping into the far post.