Allan Saint-Maximin put The Magpies in the driving seat shortly after the interval with an outstanding solo run and finish.
But The Hornets stung the hosts where it hurt them the most in the 88th minute when Joao Pedro's leaping header nestled into the top corner of the net, a goal that ended a run of six straight league defeats for Claudio Ranieri's men.
Story of the game
After crossing the ball into the box 36 times to no prevail in the embarrassing home defeat to League One side Cambridge United last weekend, Eddie Howe addressed The Magpies goalscoring issues by bringing in Chris Wood from relegation rivals Burnley for a £25 million fee.
Wood came in from the off, and joined Kieran Trippier in making his Premier League debut for Newcastle. A surprise name in the starting line-up, however, was Paul Dummett, with the full-back returning to the side after a lengthy spell on the sidelines.
After an early scare for the hosts – which involved a Watford free-kick right on the edge of the penalty area and a subsequent booking for Jonjo Shelvey – the woodwork denied them of the lead.
Four minutes later, it was Watford's turn to go close. Allan Saint-Maximin was dispossessed in the heart of the field, and Joao Pedro latched onto it. He played the ball wide to Josh King who managed to get a shot off, but he rattled the side netting.
At the midway stage of the half, it was relatively clear what the plan was for both sides: Newcastle were looking to push forward, and Watford keen to hit them on the break.
The Magpies came close twice with headed efforts from Wood and Fabian Schar in quick succession, with the gameplan of whipping as many balls into the Watford box blatantly evident at this point.
The last opportunity before the interval fell to the hosts when the ball found its way to an unmarked Sean Longstaff on the edge of the area, but he could not replicate what he did in the reverse fixture, with his shot sailing over the woodwork.
Joao Pedro strikes late to deny the Toon a big win
You felt watching the game that it would take a moment of brilliance to break the deadlock – and that is what Saint-Maximin provided Newcastle four minutes after the restart.
The Frenchman robbed Jeremy Ngakia of the ball and raced down the left-hand side before cutting onto his right-foot and firing the ball into the near-corner of the net, totally wrong-footing Hornets goalkeeper Ben Foster in the process.
Newcastle's hard work was almost undone entirely by themselves shortly after taking the lead, when a bad pass from a nervous Jamaal Lascelles was intercepted by Emmanuel Dennis, who ran past a retreating Toon defence before playing in Moussa Sissoko.
In front of the Gallowgate end – against his former club – he took aim, but lashed the ball wide of the goal.
Although it felt like the tide was turning in Watford's favour after that Sissoko miss, but Newcastle came close to doubling their lead when Jonjo Shelvey's effort from distance narrowly went over-the-bar.
But Watford's pressure paid off, and they grabbed a huge equaliser with two minutes to go in normal time.
Substitute Kiko Femenia got down the right-hand side and delivered a delicious ball into the path of Joao Pedro, who rose highest to head the visitors level, to ensure they left Tyneside with a valuable point.
And just like that, Newcastle United had done it again. They had let another lead slip.
It is now 21 points dropped from winning positions, a worrying tally for Eddie Howe, who has just witnessed his team wave another winnable game goodbye.
You can spend all the money in the world on players to try and patch up 14 years of neglect under the previous ownership in 31 days.
But one thing you cannot buy is confidence, and that is the fundamental they crave the most at this time.
This result for Watford, however, will feel like a victory for Watford and their supporters, who gleefully sang "We are staying up!" from the top of the Leazes Stand.
And with the spoils being shared, it means that The Hornets remain out of the relegation zone, while The Magpies continue to be rooted in the bottom three.
Newcastle: Dubravka; Trippier, Lascelles, Schar, Dummett; Longstaff, Shelvey, Joelinton; Fraser, Wood, Saint-Maximin. (4-3-3)
Watford: Foster; Ngakia, Cathcart, Samir, Kamara; Kucka, Sissoko, Kayembe; Dennis, King, Joao Pedro. (4-3-3)