James Milner broke the deadlock for Jürgen Klopp’s side with a penalty in the final minute of the first half and, after the Eagles tested their visitors persistently in the second period, Sadio Mane sealed three points with a stoppage-time breakaway.
It was a just reward for a resolute display by the Reds. Here are five things we spotted at Selhurst Park…
Milner the man from 12 yards
After four different players took penalties for Liverpool last season, a fifth was in charge from 12 yards during pre-season in the form of Mane.
But when the referee pointed to the spot for a foul by former Reds centre-back Mamadou Sakho on Mohamed Salah in the closing moments of the first half, it was Milner – wearing the captain’s armband – who stepped up.