Liverpool regain top spot but suffer Alexander-Arnold injury scare
Klopp's side had been knocked out of pole position by Manchester City's 2-0 victory against Everton earlier in the afternoon.
It looked as though Liverpool might end the weekend off the summit after Burnley's Dara O'Shea cancelled out Diogo Jota's opener.
But Liverpool recovered their composure in the second half as goals from Luis Diaz and Darwin Nunez lifted them two points clear of second-placed City.
However, Alexander-Arnold was forced off at half-time with a knee injury after setting a new Premier League record of 58 assists by a defender with his corner for Jota's opener.
Now Klopp is waiting to discover how long he will be without the 25-year-old England right-back.
"His knee again? Yes, it felt like that. He got it stuck in the grass and we will see. We have to assess it," he said.
"Same area in the knee. Nothing really bad, but he felt it again and we have to see.
"Trent said 'it's fine' but it's not fine (because) he feels it so we had to be careful and took him off and that's a double problem if you want: Trent is off and the other is we had no other right-backs available."
'The wild west'
In front of Liverpool's record league crowd of 59,896, following the full opening of the Anfield Road stand, the Reds responded to last weekend's damaging defeat at title rivals Arsenal.
It was a hard-fought success rather than an eye-catching performance, with Liverpool's flu and injury-hit side dragging up just enough quality to dispatch second-bottom Burnley.
Referee Tim Robinson booked five players while Klopp and Burnley boss Vincent Kompany were also shown yellow cards during a tetchy game.
That got Klopp's attention after reports on Friday that football's lawmakers IFAB are set to trial sin-bins and blue cards.
Under the plans, players would get blue cards for dissent and tactical fouls and spend 10 minutes off the pitch.
"Imagine in this game and the referee has a blue card available? It would have been the wild west. There were so many yellow cards today," Klopp said.
"I had no clue why Vincent Kompany got it. I lost it in that situation so fine, give me a yellow card. As long as I don't get a blue one and have to sit somewhere for 10 minutes!"
The breakthrough came in the 31st minute when Clarets goalkeeper James Trafford misjudged the flight of Alexander-Arnold's corner and Jota headed in his fifth goal in six games.
O'Shea produced an even better header from 12 yards from Josh Brownhill's corner, outjumping Wataru Endo to power the ball past Kelleher in first-half stoppage time.
Seven minutes after the interval, Harvey Elliott, on for Alexander-Arnold, made his first significant contribution when his low cross took a deflection off Maxime Esteve and allowed a stooping Diaz to nod in at the near post.
Nunez delivered the knockout blow in the 79th minute when he flicked a header inside the far post from Elliott's cross.