Willock's leveller in first half stoppage time at the Parc des Princes cancelled out Vitinha's early opener for the Magpies, who were already assured of a play-off berth prior to their clash with the holders.
PSG's Portuguese midfielder whipped home the opener on seven minutes to give the holders the lead, five minutes after Nick Pope had saved Ousmane Dembélé's penalty.
But Willock popped up in first half stoppage time to nod home an equaliser after latching on to a Dan Burn flick, sending United in on level terms.
A spirited second half saw Anthony Gordon and Harvey Barnes go close to grabbing a winner for the Magpies, who asked plenty of questions of Luis Enrique's illustrious team without mustering a clincher.
The result means Eddie Howe's side finish the league phase in 12th position, two points shy of the top eight, and will now face a two-legged play-off next month with progression on the line.
Head coach Howe made five changes to his side for the trip to the French capital, with Willock starting along with Anthony Elanga, Nick Woltemade, Jacob Ramsey and Dan Burn.
But a controversial opening at the Parc des Princes saw Lewis Miley penalised for handball after a VAR review inside the first minute, when Bradley Barcola's low cross was blocked by Botman and cannoned back off the United midfielder's arm via Barcola.
Pope superbly repelled Dembélé's spot kick, diving low to his left to keep it out, but could do little about Vitinha's well-taken 20-yarder five minutes later.
Miley had a brief sight of goal shortly after when Joe Willock's cross was palmed out to him by Matvey Safonov, but his left-footed shot was too high.
Luis Enrique's men dominated the first period though without forcing many further interventions from Pope, with Willian Pacho hooking a cross from substitute Désiré Doué over the bar.
But Willock's header in added time - arrowed into the corner after Burn had helped on an attempted PSG clearance from Sandro Tonali's long free kick - levelled the scores before the break.
The visitors started the second period well after that leveller too, with Jacob Ramsey testing Safonov after a swift breakaway led by Lewis Hall and Nick Woltemade. Just before the hour mark, they had the ball in the net again when Willock raced onto Hall's clipped pass and slotted under PSG's Russian goalkeeper, but it was ruled out for offside.
At the other end, Warren Zaïre-Emery sliced wide of the target and Barcola lashed over after twisting and turning in the Newcastle box.
Dembélé then tried to find the top corner to no avail with a curling shot that flew over, before the Ballon d'Or winner fired Nuno Mendes' low centre just past the upright.
Howe responded by sending on Gordon and Barnes for the final quarter as the Magpies sought a winner, and the former tried from distance but saw his effort palmed away by Safonov. The England international fed Ramsay on the counter attack, but Marquinhos got himself in the way of the shot.
The Magpies had enjoyed a spell of dominance but Vitinha's vicious effort, flashed just over, provided a reminder of PSG's threat as the contest became end-to-end. Marquinhos then felled Gordon in the box as he burst onto Burn's lay-off, but referee Slavko Vincic was unmoved.
With five minutes left, Gordon raced away down the left again and his neat flick was picked up by substitute Barnes, but Safonov did well to keep it out. Gordon and Barnes combined again moments later, with the latter finding the sidenetting from an offside position as Newcastle pushed to the end.
But they had to settle for a point in the end, with results elsewhere ensuring Howe's men missed out on automatic qualification for the last 16 - though their Champions League adventure is still far from over after an encouraging display in the French capital.
Newcastle United: Nick Pope, Lewis Hall, Sven Botman, Sandro Tonali, Malick Thiaw, Anthony Elanga (Anthony Gordon 67), Nick Woltemade (Yoane Wissa 77), Joe Willock (Harvey Barnes 67), Dan Burn (c), Jacob Ramsey, Lewis Miley
Substitutes: Aaron Ramsdale, Aidan Harris, Kieran Trippier, Will Osula, Jacob Murphy, Alex Murphy, Bruno Guimarães, Leo Shahar
