Liverpool made the most of some moments of controversy to kill off Stoke City and return to winning ways with Mohamed Salah again taking centre stage.
The Egyptian substitute took just six second-half minutes to score twice and take star billing after Sadio Mane had opened the scoring for Jurgen Klopp’s men.
Stoke were furious, however, that Liverpool goalkeeper Simon Mignolet was not red-carded late in the first half for a professional foul, having complained already that Mane’s goal should not have stood.
But some poor defending allowed Salah to cash in after stepping off the bench as Liverpool responded well to squandering leads to Sevilla and Chelsea in their previous two games.
The opening stages were blighted by poor passes, needless fouls and poor decisions that removed any possibility of flow from the game.
So the nature of the opening goal, complete with controversy and skill, enlivened an otherwise uneventful spell.
Joe Gomez chased a ball into the corner having raced forwards from right-back, but Stoke were adamant the England defender had failed to stop it crossing the byline.
The officials, however, ruled that the ball was still in play and Gomez crossed for Dominic Solanke, whose inventiveness created the chance.
He produced a neat flick into the path of Mane that left Stoke’s defenders dumbfounded, and Mane then came up with a delicate chip past goalkeeper Lee Grant.
Stoke’s response was not immediate and Grant had to make a routine save from Alex Oxlade-Chamberlain, but when they did get into the game it was through Xherdan Shaqiri.
The Switzerland forward found space regularly on the right and his invention brought some moments of promise.
The first Stoke chance came courtesy of Mame Diouf’s overhead kick and a drive by Darren Fletcher that was blocked by Dejan Lovren and the second was from Shaqiri’s clever movement, but his cross was misdirected.
A cross from Joe Allen for Stoke was then guided wide by Peter Crouch, making his first league start of the season.
Solanke should have doubled the visitors’ lead with a shot that Grant saved after the Liverpool striker had swapped passes with Roberto Firmino.
But then came the contentious moment that left Stoke seething as Mignolet raced from his penalty area to trip the advancing Diouf.
Referee Martin Atkinson awarded a free-kick but allowed Mignolet to escape with a yellow card when the case for a red appeared clear with Shaqiri blasting the free-kick into the wall.
Mane should then have added to the anger when he raced clear of a ragged Stoke defence but struck the base of the woodwork with only Grant to beat.
Stoke ought to have been level just three minutes into the second half when Shaqiri caused more problems with an inswinging cross that Liverpool struggled to deal with.
Matip cleared it partially under pressure from Crouch but it dropped invitingly for Allen, whose low shot struck a grateful Lovren and skimmed behind for a corner, which the visitors cleared.
But the hosts struggled to follow up that near-miss as Liverpool’s composed play kept Hughes’s men at arm’s length from Mignolet’s goal.
Stoke finally had some joy when the visitors failed to spot Allen’s run from midfield to the byline, with the Welshman forcing a corner.
But the flag-kick was cleared by the Reds who caused problems on the break, with Stoke forced to clear hurriedly away from their six-yard box after a pass from Alberto Moreno.
The Potters claimed another free-kick on the left but the inswinging delivery from Darren Fletcher was punched clear by Mignolet.
There was more anger with 23 minutes remaining when Stoke defender Bruno Martins Indi produced a crude block with his arm on Oxlade-Chamberlain, who reacted by shoving the Dutchman in the chest.
Both men were booked and, in the aftermath, Stoke should have drawn level.
A cross by Erik Pieters was headed down by Crouch for Allen, who blasted over from 12 yards.
With 13 minutes remaining Liverpool ended any doubts about the win as Mane crossed from the right and Salah volleyed home.
Six minutes later Salah added the third when he beat Pieters to a diagonal ball, raced clear and fired low past Grant.
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