- Andrej Kramarić penalty saved by Simon Mignolet.
- Trent Alexander-Arnold scores first Liverpool goal from free-kick.
- Harvard Nordtveit deflects James Milner cross into own net on 75 minutes.
- Mark Uth nets consolation for Hoffenheim.
- Philippe Coutinho out with a back injury as rumours swell regarding Barcelona move.
- Liverpool unchanged from Premier League draw with Watford.
- Hoffenheim finished fourth in the Bundesliga last season.
- Julian Nagelsmann's side playing their first ever Champions League match.
- Bundesliga side started campaign with Germany Cup win over Erfurt.
Well that brings an end to coverage of this Champions League play-off first leg. We'll be back with coverage of the second leg of this tie in eight days time when Liverpool will hope to convert their position of dominance.
Before then we turn our attention back to the Spanish Super Cup, with Real Madrid and Barcelona meeting for a second time after their eventful clash over the weekend, which saw Zinedine Zidane's side claim a 3-1 win.
But until then, let me wish you a very good evening.
Full time: Hoffenheim 1-2 Liverpool
Liverpool put one foot in the Champions League group stage but they were pushed all the way but Hoffenheim. After Andrej Kramaric's missed penalty, Trent Alexander-Arnold scored spectacularly from a free-kick.
James Milner's deflected cross doubled the lead before Mark Uth's fine strike cut the deficit and gives Hoffenheim hope heading into the second leg. Jurgen Klopp's defensive problems have not been solved but he will be delighted with the club's first win of the campaign.
Free-kick for Hoffenheim, 25 yards from goal and they load the box looking for an equaliser. Benjamin Hübner finds himself completely unmarked six yards out but he blazes his header over. Liverpool survive, but I'm not sure how.
GOAL! Hoffenheim 1-2 Liverpool (Mark Uth)
Hoffenheim set up a grand stand finale with a fine late goal which could prove vital in eight days time. Pavel Kadeřábek plays a fine cross-field pass and while Liverpool defender stop and appeal for offside, substitute Mark Uth brings the ball down on his chest and hammers the ball into the corner with aplomb.
Liverpool celebrate going 2-0 up in Germany.
Salah and Mane link-up in a sign of things to come but the Senegal forward thrashes wide. Dominic Solanke on for his Liverpool debut, replacing Roberto Firmino.
Simon Mignolet is making a fine claim for the man-of-the-match award. A penalty save and now he keeps Hoffenheim from getting a consolation as Wagner heads back to Nadiem Amiri, whose strike into the ground is pushed away by the Belgian.
If Liverpool want a third goal and a stroll around Anfield next week then it is very much there for the taking. Firmino and Mane combine down the left but his cross can't find Salah.
GOAL! Hoffenheim 0-2 Liverpool (James Milner)
Liverpool should be out of sight as they double their lead. James Milner is released down the left and though he goes to cross it takes wicket deflection off Nordtveit and it loops into the top corner. It will go down as an own goal, but the guile from the ex-England man was magnificent.
Now Dejan Lovren's point blank header is kept out. Liverpool can put this tie to bed tonight if they put their mind to it.
Mohamed Salah should double his Liverpool tally but Baumann saves again from a tight angle. Will Liverpool rue missing these chances?
The man of the moment has Liverpool in his blood. If you didn't already know, check out this picture of him alongside Jamie Carragher as a club mascot.
Hoffenheim scored more goals from set-pieces than any other in the Bundesliga last season and they are peppering Mignolet and the Liverpool back-four with a succession of corner - but the Reds come out of the spell unscathed.
It is captain Jordan Henderson who makes way for Milner, who will move to midfield.
Liverpool are being awfully wasteful as Hoffenheim continue to throw players forard. The Bundesliga side are here for the taking you feel.
James Milner coming on for Liverpool.
Here is another look at that Trent Alexander-Arnold goal for Liverpool which sees them on course for a first leg lead
Booking for Trent AA, much to the delight of the home faithful whose side are huffing and puffing but are yet to find a way through this Liverpool rearguard.
Mane is everywhere at the start of this second half and he almost puts Liverpool two-up, shooting from a tight angle and forcing a save from Baumann, which somehow doesn't fall to an onrushing player.
Ball in the net for Hoffenheim but it isn't going to count. Wagner releases Gnabry and he makes no mistake, beating Mignolet at his near post with a fabulous strike- but the goal is ruled out for offside. And the replay clearly shows the German youngster is a good three yards off.
Trent Alexander-Arnold celebrates scoring his first Liverpool to put them ahead.
What a chance to double the lead. Mane gets away from Bičakčić down the left and his cross finds Firmino, but his shot towards goal is saved low by Baumann.
Both sets of players back out and we're underway in the second half. No changes at the break.
Half time: Hoffenheim 0-1 Liverpool
What a thorougherly entertaining half of football. A missed penalty, a sensational free-kick and loads of missed chances ends with Liverpool ahead with a critical away goals courtesy of Trent Alexander-Arnold's blistering free-kick. Hoffenheim look a threat every time they get the ball in the final third but while it might not be pretty for Liverpool they lead in this must-win tie.
Liverpool's lead hangs by a threat as Hoffenheim twice go close. First, Lovren is all over the place in the air as Kramaric nods on to Gnabry, who gets gaoled and produces a fine save from Mignolet. From the rebound the ball falls to Wagner, who glances the post with Mignolet stranded.