It was a huge Merseyside derby, with the Reds and the Blues desperate for points for very different reasons.
Liverpool struggled to get their usual game going as Everton defended resolutely and mastered the dark arts, but they got the breakthrough with a rare Robertson header.
Substitute Divock Origi sealed the victory in the dying minutes, further etching his name into Reds folklore.
It was Robertson (8.3) who was the richly-deserved recipient of the highest average rating by far, on a day when he was an unlikely hero.
The Scot opened the scoring with a well-taken header after a nerve-racking opening hour or so, celebrating wildly in front of the Kop.
Ian Doyle of the Echo felt Robertson was “regularly an outlet down the left” for Liverpool, standing tall while others struggled.
Meanwhile, TIA’s Henry Jackson felt the left-back’s strike was a “potentially huge moment” in the Reds’ season.
Matip produced an 89 percent pass completion rate, according to FotMob, who also highlighted that he won four out of his six tackles.
Next up was Virgil van Dijk (7.1), after the Dutchman cruised through proceedings in typically unruffled fashion.