Kobbie Mainoo gave the Reds a deserved half-time lead, slotting home after finding space in the box, but the Magpies responded at the beginning of the second half through Anthony Gordon.
Amad's half-volley hurtled into the net to make it 2-1, before substitute Rasmus Hojlund established a two-goal cushion, with that effort proving vital when Lewis Hall lashed in a late goal of his own.
There were a few nervy moments along the way, but Erik ten Hag's men closed out the game to take all three points, a tally which brings us level with Newcastle and keeps us in the hunt for European qualification on the final day of the Premier League season.