The visitors dominated the first 45 in North London and were good value for their half time lead, with Anthony Elanga instrumental in forcing a couple of early corners before crossing for Sven Botman to head over.
Xavi Simons dragged a shot through Kieran Trippier's legs and into the sidenetting for the hosts, but Willock went even closer for the Magpies, firing just wide of the target after some neat build-up play involving Harvey Barnes, Anthony Gordon and Bruno Guimarães.
Elanga could have felt a little aggrieved not to have an assist to show from his bright start, with Barnes backheeling a low cross from the Swedish international straight at Spurs stopper Guglielmo Vicario.
Jacob Ramsey, brought back into the side by head coach Howe following Saturday's defeat to Brentford, latched on to a Dan Burn knock-down just over quarter of an hour in, but didn't connect cleanly with the strike. Just before the half hour, he took aim again, whistling a powerful shot just past the upright.
Just before the break, United thought they had deservedly moved in front. Ramsey's through ball released Willock down the middle, and the former Arsenal man cut inside and buried a shot beyond Vicario. It was a superb finish but after a protracted VAR check, the goal was ruled out for offside, with Willock's forehead ever so fractionally beyond the last man when Ramsey played him in.
The disappointment didn't last long though, and Willock had a hand in Thiaw's opener. His cross for the German international was an excellent one, and while the centre back's header was saved by Vicario, Thiaw followed in to prod home the deadlock-breaker deep in stoppage time.
Head coach Eddie Howe made four changes to his side for the trip to the capital, with Burn, Ramsey, Elanga and Gordon coming into the starting 11 at the expense of Lewis Hall, Sandro Tonali, Jacob Murphy and Yoane Wissa.
**Newcastle United:** Nick Pope; Kieran Trippier, Sven Botman, Anthony Gordon, Harvey Barnes, Malick Thiaw, Anthony Elanga, Joe Willock, Dan Burn, Bruno Guimarães (c), Jacob Ramsey
**Substitutes:** Aaron Ramsdale, Lewis Hall, Sandro Tonali, Yoane Wissa, Will Osula, Jacob Murphy, Nick Woltemade, Alex Murphy, Leo Shahar