Luke Supyk poked home to give United's National League neighbours a first half lead at Gateshead International Stadium.
But Williams couldn't get out of the way of Lewis Hall's cross and turned it past goalkeeper Adam Desbois late on to pull Eddie Howe's side level in their second outing of pre-season, following last weekend's behind-closed-doors win over Darlington.
Magpies fans who headed across the river will have been encouraged by the sight of defender Fabian Schär back in action for the first time since he suffered an ankle injury in January, while summer signing Sean Steur turned in a composed, promising display in central midfield after a crowd of over 7,000 observed a minute's silence in memory of Kevin Keegan.
United had the better of the chances in the opening half but went in behind at the break. Under two minutes into the contest, forward Sean Neave - who debuted for Howe's first team in the Champions League last term - took aim from a tight angle and forced a fine one-handed save from Heed stopper Desbois, who then caught Joe Willock's deflected shot moments later.
It was an impressive stop from the hosts' goalkeeper, who was the busier of the two custodians in the first half, with Nick Pope watching Josh Home's glancing header from Billy Chadwick's inswinging cross drift wide of his upright at the other end.
After Desbois got a touch to a Neave strike across the face of goal, Hall cleared the crossbar with a dipping effort moments later, but just after the half hour Lee Cattermole's men took the lead. Chadwick's free kick on the edge of the box was deflected and Supyk pounced to prod past Pope from close range.
Harvey Barnes couldn't home a leveller from close range before the halfway point, though, with Desbois recovering to smother at the second attempt, while Supyk's shot from range bounced well wide just after the restart.
But the Magpies looked livelier at the start of the second half, with Desbois again in the thick of the action to thwart Neave before Hall thought he might have had a penalty following a sliding challenge from David Ferguson, who was deemed to have played the ball.
After Steur saw his strike charged down, Howe began to make some changes in the final half hour, with Miodrag Pivaš, Ewen Jaouen, Mason Miley and Matheos Ferriera all entering the fray. The latter had a sight of goal just a few moments after coming on, but shot straight at Desbois from inside the box.
Jacob Murphy had a go from distance soon after before wingers Trevan Sanusi and Seung-soo Park were introduced as the visitors looked for a leveller, and they finally found a way through when Hall latched on to Jacob Ramsey's terrific through ball and his cutback was inadvertently turned in by Williams to snatch a draw.
United continue their pre-season preparations at Bristol City on Wednesday night (kick-off 7.30pm BST).
Newcastle United: Nick Pope (Ewen Jaouen 69), Lewis Hall (Vakhtang Salia 82), Fabian Schär (Miodrag Pivaš 60), Harvey Barnes (Seung-soo Park 77), Sean Steur, Jacob Murphy (Trevan Sanusi 77), Joe Willock (Dylan Charlton 82), Alex Murphy, Jacob Ramsey (Anthony Munda 82), Leo Shahar (Mason Miley 69), Sean Neave (Matheos Ferreira 69).
Subs not used: Mark Gillespie, Aidan Harris, Luke Craggs, Rory Finneran.
