James Milner's penalty and Sadio Mane's late strike sealed a 2-0 win for Liverpool against Crystal Palace, who had Aaron Wan-Bissaka sent off on Monday Night Football.
It had been an even opening period when Mamadou Sakho caught the ankles of Mohamed Salah in the area on the cusp of half-time - sending him down - and Milner put the resulting spot-kick past Wayne Hennessey.
Salah was involved again as Palace ended the game with ten men when Wan-Bissakka brought down the Egypt international just outside the box in the 75th minute. It was a straight red card for the youngster, meaning he will miss the next three fixtures.
Mane rounded off the victory in the third minute of added time as Liverpool hit their hosts on the break, with the Senegal forward slotting home to give Liverpool a second win of the season.
Crystal Palace: Hennessey (7), Wan-Bissaka (6), Van Aanholt (7), Tomkins (6), Sakho (6), Schlupp (5), McArthur (6), Milivojevic (6), Townsend (6), Zaha (6), Benteke (6).
Subs used: Sorloth (5), Ward (4), Meyer (n/a).
Liverpool: Alisson (7), Alexander-Arnold (7), Van Dijk (8), Gomez (7), Robertson (7), Wijnaldum (6), Milner (7), Keita (7), Salah (7), Mane (7), Firmino (6).
Subs used: Henderson (6), Lallana (n/a), Sturridge (n/a).
Man of the match: Virgil van Dijk.
It was a fairly quiet first half until the 23rd minute when Naby Keita nicked the ball around Andros Townsend before taking a few strides and releasing a superb long pass for Salah. The forward tried to chip over Hennessey but under pressure, he sent the ball flying high into the crowd.
Palace went close 90 seconds later when Townsend fired a curling effort towards goal but it smashed off the top corner of the crossbar. Wilfried Zaha attempted to net the rebound but it hammered off the back of Joe Gomez before going behind for a corner.
Both sides named an unchanged XI from their opening weekend fixtures. Max Meyer was named on the bench for Crystal Palace while Fabinho and Loris Karius missed out on the matchday 18 for Liverpool.
Liverpool opened the scoring just before half-time through Salah, who was tripped in the area by Sakho, with referee Michael Oliver instantly pointing to the spot despite protests from the defender. Milner dispatched coolly past Hennessey.
The second half began at a pace, with Salah rounding the oncoming Hennessey in the box early on but failing to chip home before Keita fired the cut-back from his team-mate just wide. At the other end, Alisson was called into action eight minutes after the restart as Luka Milivojevic curled a free-kick his way, but the Brazilian made a leaping save.
With 15 minutes to play, Crystal Palace went down to ten men as Wan-Bissaka was given his marching orders. As Salah raced towards goal, the 20-year-old caught him around the ankles just outside the area and was shown a straight red card.
Liverpool pushed for another as the game drew to a close and made the breakthrough in the 93rd minute. After clearing a Palace corner, Salah burst down the field before laying the ball off to Mane. He continued the run, shrugging off a challenge from Patrick van Aanholt and rounding the oncoming Hennessey before slotting home.
- Liverpool won their 34th Premier League game played on a Monday - only Man Utd (43) and Arsenal (36) have more victories.
- Roy Hodgson suffered his 100th defeat in the Premier League as a manager (W87 D65 L100).
- Aaron Wan-Bissaka is the youngest Crystal Palace player to be shown a red card in the Premier League (20 years, 267 days).
- James Milner extended his current record for the most Premier League games scored in without losing any of them (48 Games: W38 D10 L0).
Notes for Southgate
The England manager and his assistant, Steve Holland, were in attendance and Trent Alexander-Arnold and Joe Gomez put in a good shift in defence. Jordan Henderson also made a solid 23 minute cameo with Daniel Sturridge getting a few minutes - if that - towards the end. For Crystal Palace, Andros Townsend did well although Aaron Wan-Bissaka was sent off, and could have scuppered a chance to be named in Southgate's next England side.
Roy Hodgson: "I considered us unlucky to have been on the wrong end of refereeing decisions, but that's my opinion. Other people can have theirs.
"Really and truly, I don't like talking about refereeing decisions. I can't change them, they obviously irritate me, they obviously anger me when it costs the team points but then I'm just like every other manager in football from Sunday league up to the Premier League."
Jurgen Klopp: "They caused us as many problems as possible with these long balls and then if you win the second one, they try to get in behind really quickly in one-on-one situations with Zaha.
"We were there and helped each other to avoid big problems but it was not a brilliant performance from us tonight. A lot of players can play 70 per cent or 80 per cent better; it would have helped but we worked really hard and that's absolutely OK. I'm happy with the performance and very happy with the result."
Could VAR have made a difference?
VAR would probably have been used a few times. Of course, there is the first-half penalty that was awarded and referee Oliver may have wanted to consult a replay before giving - or not giving - the spot-kick.
There was also Wan-Bissaka's red card. Salah appeared to kick the ball away before the tackle, meaning there could have been a case for it not to have been a straight red card. Again, Oliver could have consulted a replay and his colleagues to make a decision.
Man of the match - Virgil van Dijk
It was another Premier League clean sheet for Liverpool, and Van Dijk was a big part of that. Crystal Palace had their fair share of chances - particularly in the first half - and he was key in making headers, tackles and blocks to keep Liverpool's 100 per cent record intact.
Crystal Palace are live on Sky Sports again next weekend as they travel to Watford on Renault Super Sunday. Liverpool will be in action on Saturday, welcoming Brighton for the evening kick-off.