Liverpool saw their unbeaten run of 18 matches come to an end in Swansea as the Premier League's bottom club secured a shock win at the Liberty Stadium.
Alfie Mawson's header in the 40th minute proved to be the game's only goal, the defender punishing Liverpool's failure to clear a corner just before the break.
Jurgen Klopp's Reds did everything but score, banging away in search of an equaliser but ultimately coming up short. Liverpool lose track on the top two as a result, but remain in fourth place after Tottenham's draw at Southampton yesterday.
Liverpool gave £75million signing Virgil van Dijk a Premier League debut and it was the centre-back's header that eventually fell for Mawson to sweep in the opener in the 40th minute.
Klopp's side had plenty of chances to get on the scoreboard, Sadio Mane firing wide in first-half stoppage time and Mohamed Salah seeing his free-kick tipped over magnificently by the impressive Lukasz Fabianski.
There proved to be no way through for Liverpool, who saw Roberto Firmino hit the post with a header deep into stoppage time - Adam Lallana unable to convert the rebound - as they failed to claim a sixth straight win in all competitions for the first time under Jurgen Klopp.
Carvalhal deployed a three-man defence but a lofted pass from Emre Can – who was wearing the captain's armband – quickly bypassed it in the 10th minute, though Mane's first touch enabled Fabianski to come off his line and smother.
Van Dijk went close with a header before turning creator with a chipped pass in behind for Salah, who lashed a left-footed volley high and off target as it dropped over his shoulder.
Alex Oxlade-Chamberlain drilled an effort straight at Fabianski and Liverpool were punished for their profligacy five minutes before half-time. Van Dijk was unable to clear a corner sufficiently and, after the ball bounced off Federico Fernandez, Mawson fired just Swansea's second shot of the half into the bottom-left corner.
Mane had a chance to equalise in first-half stoppage time but he lost his footing as Salah's cross came in from the left and volleyed wide.
Liverpool found it tough to test Fabianski despite dominating possession after the restart, Salah curling outside the right-hand post before Kyle Naughton's excellent challenge denied Andrew Robertson a one-on-one with the goalkeeper.
When Klopp's men did get a shot on target they found Fabianski in fine form, the Poland international leaping to his right and pushing Salah's free-kick behind on the hour.
Lallana and Danny Ings entered the fray for the visitors, in place of Oxlade-Chamberlain and Georginio Wijnaldum, and the former Burnley striker forced Fabianski to make a save low to his left with a cross-goal effort 13 minutes from time.
Liverpool piled on the pressure in the closing stages but Can and Salah wasted stoppage-time opportunities before Firmino almost broke Swansea hearts.
The Brazilian had scored five goals in his last three Premier League appearances against Swansea but he was unable to add to his tally as his 94th-minute header came back off the upright and Lallana could not convert on the follow-up from inside the six-yard box.
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