An injury to Fabinho overshadowed Liverpool's unconvincing 2-0 Champions League win over Midtjylland, with Diogo Jota and Mo Salah on target.
Jota fired into an empty net from the Reds' best move of the game - to score the club's 10,000th goal in history - 10 minutes after half-time when man-of-the-match Trent Alexander-Arnold teed up the Portuguese forward for a tap-in.
That would prove to be their only shot on target until injury-time, but Liverpool had already been made to sweat before half-time when Fabinho was forced off with what appeared an injury to his hamstring, leaving Rhys Williams the only senior defender able to replace him with half an hour played.
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- How the teams lined up | Match stats
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Jurgen Klopp had left Roberto Firmino, Salah and Sadio Mane on the bench but even the introduction of the latter pair with an hour played made little improvement to their attacking play.
Liverpool were nearly made to pay when substitute Evander fired just wide before Anders Dreyer went even closer late on, but the hosts added some gloss to a poor performance when Salah converted a penalty he had won himself in injury-time to keep up their perfect start to their Group D campaign.
Liverpool: Alisson (6), Alexander-Arnold (8), Gomez (5), Fabinho (6), Robertson (6), Milner (6), Henderson (6), Shaqiri (6), Minamino (5), Origi (5), Jota (7).
Subs: Rhys Williams (6), Wijnaldum (6), Salah (7), Mane (5), Firmino (n/a).
Midtjylland: Andersen (6), Andersson (7), Sviatchenko (7), Scholz (6), Paulinho (6), Onyeka (6), Cajuste (7), Dreyer (7), Sisto (5), Mabil (5), Kaba (5).
Subs: Anderson (5), Evander (6), Kraev, Pfeiffer (n/a).
Man of the match: Trent Alexander-Arnold
Sluggish Liverpool labour to down Danes
Midtjylland came into Tuesday's game having been hammered 4-0 by Atalanta in their first-ever Champions League group match a week ago, but Klopp insisted the Danish champions would give his side a run for their money - and he was not mistaken.
Star-man Dreyer came close to proving his point with less than three minutes on the clock when he brought down Alexander Scholz's long ball and pulled a strong low save out of Alisson.
Liverpool's changed front three looked uncomfortable as a trio and it was Alexander-Arnold who looked most likely to create an opening, with Takumi Minamino missing a low cross altogether before Joel Andersson stopped another from reaching him after a good run from the Liverpool right-back.
But a match-ending injury to stand-in defender Fabinho on the half-hour mark would prove a bigger concern for the Reds, with Williams, who a year ago this week was starting in defence for Kidderminster in the National League North, his only available replacement.
Perhaps more cautious to protect the inexperienced defender, Liverpool looked more solid in the last throes of the opening period, and saw Jota and Minamino nod Alexander-Arnold crosses wide before going in goalless at the break.
Georginio Wijnaldum replaced Jordan Henderson as Liverpool's second change at the interval before they upped their level of intensity from the restart, and 10 minutes after half-time finally looked like the Liverpool which Klopp has developed in recent years to open the scoring.
It was little surprise Alexander-Arnold was at the heart of the move, timing his run from a one-two with Xherdan Shaqiri to perfection to stay onside before squaring for a simple Jota finish.
- Liverpool made four changes from their Sheffield United win, bringing in Xherdan Shaqiri, Takumi Minamino and Divock Origi for Mo Salah, Roberto Firmino and Sadio Mane.
- Midtjylland changed five players from their win at Brondby on Saturday, including a start for back-up goalkeeper Mikkel Anderson due to Jasper Hansen's injury.
Mane and Salah were introduced five minutes later but their introduction, likely sooner than Klopp would have liked, did not have the desired effect as Midtjylland grew back into the game after the setback of the goal.
With 13 minutes remaining, substitute Evander fired wide after shaking off Joe Gomez before the defender was again sluggish as Dreyer drifted past him and fired a glorious chance to level into the side-netting.
Paulinho's clumsy foul on Salah from a long ball in injury-time gave Liverpool the chance to add a second goal they could barely claim they deserved in the final minute, with the Egyptian getting up to bury the spot-kick beyond Mikkel Anderson and ensure the Reds stay top of their group.
What the manager said...
Liverpool boss Jurgen Klopp told BT Sport: "[Fabinho's injury] is exactly the last thing we needed. What can I say? I know he felt his hamstring, that's not good, he didn't feel it that much, he said he could have played on but with no sprints any more so that doesn't help in that position obviously. We'll see, we have to do a scan and then we'll know more, but that's not good, of course.
"The problem then is the challenges in the moments when you have to be really lively without the ball as well, and then you have to calm down. Tonight, in too many situations that did not happen for us.
"It was a bing-bing, bing-bing game pretty much, with two goals we scored, three big chances for them, I would say. We had a couple more where we could have scored, but it never became an easy one, it was a proper fight until the end."
Man of the match - Trent Alexander-Arnold
Sometimes it can be difficult to pick a man of the match. Not tonight. Alexander-Arnold was head and shoulders above anyone else on the pitch, running the show from right-back and making both goals.
He had no problems up against one of Midtjylland's dangermen Mabil, who was removed with 25 minutes to go, and was Liverpool's most creative outlet by a mile.
Had Minamino and Jota had their shooting boots on more regularly, he could have had a quartet of assists, but he can rest easy after a superb double which played a major part in Liverpool's win.
- FC Midtjylland became the 17th team to play their first-ever UEFA Champions League away game against an English side - with all 17 failing to win and 15 losing.
- Liverpool failed to register a single first-half shot on target for the first time in 51 home games in all competitions, since October 2018 against Manchester City in the Premier League.
- Excluding qualifiers, FC Midtjylland have lost eight of their 10 away games in European competition (W1 D1).
- Liverpool started without any of Mohamed Salah, Sadio Mane or Roberto Firmino for the first time in the Champions League since 2015-16 and just the 40th time in all competitions since then (P40 W17 D16 L7).
- Since his Liverpool debut in October 2016, Trent Alexander-Arnold has registered 35 assists in competitions, with no Premier League defender managing more in that time (also 35 for Andrew Robertson).
Next up, Liverpool host West Ham at Anfield in the Premier League on Saturday Night Football live on Sky Sports Premier League from 5pm; Kick-off at 5.30pm.