Sadio Mane scored the opener in the 12th minute but Sam Allardyce made his mark on his West Brom managerial debut as Semi Ajayi grabbed a late equaliser.
So, who were the best and worst performers from both sides?
✔️ GOOD PERFORMANCE
Sadio Mane: 7.3
A moment of magic from Mane had seemed set to be the difference over a resilient West Brom side playing in the image of their new manager.
The Senegalese star ran onto a through ball from Joel Matip before brilliantly controlling it on his chest and volleying past Sam Johnstone all in one manoeuvre.
He was Liverpool's only consistent danger in attack, having three shots and eight touches in the penalty area.
❌ BAD PERFORMANCE
Andrew Robertson: 6.6
Regarded by many as the best left back in the world, the Scotland full-back was way below his usual levels on Sunday.
His sloppiness eventually led to the concession of multiple corners which resulted in West Brom's late equaliser.
He made more crosses than anyone else on the pitch but they rarely reached their destination as Liverpool dropped their first home points of the season.
⭐ STAR MAN
Joel Matip: 8.3
The Cameroonian only lasted an hour before he was forced off with what appeared to be a groin problem, and he will be sorely missed based on this showing.
Matip was a tower of strength at the back and completely dominated the West Brom attackers. He won all of his tackles, seven of his eight duels and four of his five aerials.
He also used the ball wonderfully, completing 94% of his passes and delivering the assist for Mane's goal with a brilliant through ball.
When he came off, Liverpool suddenly started to struggle and they eventually conceded an equaliser to drop two costly points.