However, in claiming six points from successive trips to Stoke and West Brom, they have triumphed at two of the league's toughest venues where the hopes of many big teams have been sunk in recent years.
Liverpool could still be passed by Manchester City if they win their game in hand but they hold a healthy lead over Everton, Manchester United and Arsenal.
Brazil global Roberto Firmino scored the only goal of the game just shy of half-time as he headed home from James Milners free kick. If the ball is in the air, what can you do?
The visitors were under pressure early on but Hal Robson-Kanu could only volley wide after being played in during the third minute.
Roberto Firmino headed home at a free kick in first-half stoppage time.
Firmino crossed for Coutinho, who sent a hard shot wide at the far-post.
The Brazilian converted a flick-on from Lucas Leiva to seal a fifth win in their last seven games for Liverpool.
Goalkeeper Ben Foster ventured up for a stoppage-time corner to try and improve this record but found himself stranded on the right wing.
It took until the 80th minute for the Baggies to really threaten when substitute Rondon turned Matip and fed in Phillips, who saw his strike saved from inside of the box by the legs of Mignolet.
But, having already racked up some terse tussles with Albion boss Tony Pulis during his time in the Premier League, Klopp found it impossible to relax.
Klopp said he felt his side's performance after the break had been an improvement on their efforts before it, adding: "In the first half, we didn't play too good [in terms of] football". Liverpool substitute Alberto Moreno eyed up West Brom's unguarded goal but, like all other attempts during the second half, his shot was off target.
- Roberto Firmino has now surpassed his Premier League goal tally from last season (10 in 2015-16, 11 in 2016-17).