The 25-year-old displayed stunning control to take a long ball onto his chest before rounding the goalkeeper and firing his 10th goal of the season.
That levelled an equally memorable volley from Yohan Cabaye.
Liverpool had enough chances to secure a victory, while Newcastle was reduced to 10 men in the closing stages when Fabricio Coloccini was dismissed for a ugly tackle on Suarez.
The game was preceded by a presentation by Gary McAllister to Steven Gerrard on the day of his 600th appearance for Liverpool — a figure reached by only nine men before him.
It is a sign of our No. 8’s standing in English football that even the Newcastle supporters stood to applaud, while Jamie Carragher thinks his friend can now rightly claim to be the greatest player in Liverpool’s 120-year history.
It’s difficult to argue, though even Gerrard would need a handsome slice of luck to score from 60 yards. His attempt to do just that was among the highlights of a first half which Liverpool controlled but Newcastle won.
Within a minute of kick-off Raheem Sterling drew a foul from Vurnon Anita in an attacking position, inviting Gerrard to place the ball and force Tim Krul into a desperate punch.
A few seconds passed before Sterling collected possession again. This time he executed a one-two with Nuri Sahin, skipped past a man and crossed low into the six-yard box. Newcastle cleared their lines but Alan Pardew was already issuing fresh instructions from his technical area.
The assault continued. Suarez curled agonisingly wide from a free-kick and then worked a yard in the box before being denied by the legs of Krul.
Newcastle launched a few long-range efforts of its own, but Demba Ba was enjoying none of the service that had helped him score six in six prior to this encounter.
Suarez beating Steven Taylor to a header in the Newcastle box just about summed things up, but his effort went wide and the scoresheet remained blank.
Suso then shimmied into the box but a deflection saw the visitors escape. They would have been the happier side at a goalless first half, but after 43 minutes Cabaye sent the travelling supporters wild with an angled volley into the top corner right in front of the Kop.
Not since December had Liverpool — who was again without Pepe Reina and Glen Johnson — come from behind to win a league game. Their opponents that day? Newcastle.
A succession of corners early in the second period boded well for those in Red, while Pardew was forced to replace the injured Ba with Sammy Ameobi.
Suarez made Krul stretch to save a snapshot from 18 yards as the Kop grew impatient. This was Liverpool’s chance to climb into the top half of the table for the first time this season.
Sahin then came close and when Newcastle mounted a counter-attack, Martin Skrtel was there with a clean tackle inside the box.
The leveller came in the 67th minute, and was arguably worth the wait. It was Jose Enrique who rainbowed a long ball over the top and into the run of Suarez. The Uruguayan was majestic in doing the rest, getting ahead of his marker, controlling on his chest, rounding the goalkeeper and finishing into an empty net.
Three minutes later it was almost 2-1 when Suarez wriggled free of a couple of defenders before putting it on a plate for substitute Jonjo Shelvey, who held his head in hands after failing to connect sufficiently.
Another superb chance was then wasted as Suarez played Sterling clean through. The 17-year-old hesitated a fraction too long, allowing Taylor to slide in and block the shot.
Newcastle’s chances of holding on were hindered in the 84th minutes when skipper Coloccini received a straight red card for a landing his studs on the back of Suarez’s leg.
Liverpool could not capitalise, however, with Shelvey heading straight at the ‘keeper and then forcing Krul to tip onto the crossbar in the game’s final opportunities.
Liverpoolfc.com journalists’ man of the match: Luis Suarez.