On a standout day for the Premier League's underdogs, Manchester City, Arsenal, Chelsea and Tottenham all dropped points.
Manchester City were held 2-2 by Crystal Palace, further boosting Liverpool's title hopes, after Tottenham drew 0-0 at Watford.
Arsenal's underwhelming form under new manager Mikel Arteta continued in a 1-1 draw with Sheffield United, while Chelsea looked headed for a draw until Isaac Hayden headed in to give Newcastle a 1-0 win in stoppage time.
Not even Sergio Aguero's fearsome scoring form could earn City a win over a tenacious Crystal Palace team.
With City staring at a possible defeat courtesy of Cenk Tosun's 39th-minute goal for Palace, Aguero scored twice in the last 10 minutes, taking him to six goals from his last three league games. However, Palace levelled in the 90th when Wilfried Zaha's ball went in off Fernandinho.
"I think we did everything," said City manager Pep Guardiola. "They defended so deep. We knew that, so we attacked — crosses and corners, put the ball inside. They didn't do much but they win one point."
On a day of draws, Chelsea looked on target for another point in the last game. But in the fourth minute of stoppage time, Newcastle won a corner to roars from their fans. Matt Ritchie took the set piece poorly, but Chelsea could only clear it to Allan Saint-Maximin, who swung in another cross from deep which Hayden headed in.
"I don't score many in the Premier League — or at all. I think it came off the side of my face," said Hayden.
"You don't always create clear-cut chances against Newcastle — fair play to them, they defend with everything — but we absolutely controlled it," Chelsea manager Frank Lampard said. "If you don't score, you're always vulnerable to that sucker punch."
With Pierre-Emerick Aubameyang suspended, Arsenal lacked the attacking firepower to see off Sheffield United in a 1-1 draw.
John Fleck salvaged a draw for United with a bouncing shot in the 83rd minute after two 18-year-olds had combined for Arsenal's opening goal. Gabriel Martinelli was the scorer, knocking the ball in from close range after fellow youngster Bukayo Saka's cross was deflected and looped over the Sheffield defence.
Tottenham were Champions League finalists last season but slipped further away from qualifying for next season's competition with a 0-0 draw at Watford. A penalty save by goalkeeper Paulo Gazzaniga kept Spurs in the game before a goal-line clearance from Watford's Ignacio Pussetto stopped Tottenham sneaking a win in stoppage time.