Sean Longstaff provided Newcastle with the lead twice in the first half, but Luton responded on both occasions, first with Gabriel Osho and later with Ross Barkley.
Despite trailing 1-0 at halftime due to Neal Maupay's goal, Spurs made a blazing start to the second half, scoring three quickfire goals to overturn the deficit and secure a crucial victory.
On the 89th minute, Forest substitute Taiwo Awoniyi scored a goal, but Arsenal maintained their lead, securing consecutive victories as they head into a crucial clash with Liverpool at Emirates Stadium on Sunday.
Newcastle's victory on Tuesday night halted their four-game losing streak in the Premier League and handed Unai Emery's side their first home defeat of the season.
At halftime, the teams were tied after Erling Haaland converted a penalty and Manuel Akanji scored with a header, while Thiago Silva and Raheem Sterling also found the back of the net.
The challenge for Everton at Anfield became significantly tougher as defender Ashley Young received his marching orders in the 37th minute, with two yellow cards issued for fouls on Liverpool winger Luis Diaz.
Pep Guardiola returned to the dugout for his team. They fell behind when James Ward-Prowse deflected Vladimir Coufal's cross beyond Ederson in the 36th minute.
